LMFDB - Embedded newform 605.2.m.c.112.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(112,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.112"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,6,0,-2,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			112.3
Character	$\chi$	$=$	605.112
Dual form			605.2.m.c.578.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.221702 + 0.435114i) q^{2} +(0.178235 - 1.12533i) q^{3} +(1.03540 - 1.42510i) q^{4} +(-0.207538 - 2.22642i) q^{5} +(0.529164 - 0.171936i) q^{6} +(2.88051 - 0.456227i) q^{7} +(1.81429 + 0.287355i) q^{8} +(1.61856 + 0.525902i) q^{9} +(0.922733 - 0.583903i) q^{10} +(-1.41917 - 1.41917i) q^{12} +(-2.60754 + 1.32861i) q^{13} +(0.837124 + 1.15220i) q^{14} +(-2.54245 - 0.163276i) q^{15} +(-0.811484 - 2.49749i) q^{16} +(4.69392 + 2.39167i) q^{17} +(0.130010 + 0.820851i) q^{18} +(-3.31646 + 2.40955i) q^{19} +(-3.38776 - 2.00946i) q^{20} -3.32285i q^{21} +(-2.12046 + 2.12046i) q^{23} +(0.646740 - 1.99046i) q^{24} +(-4.91386 + 0.924132i) q^{25} +(-1.15619 - 0.840024i) q^{26} +(2.43208 - 4.77322i) q^{27} +(2.33230 - 4.57740i) q^{28} +(-2.13957 - 1.55449i) q^{29} +(-0.492622 - 1.14246i) q^{30} +(-2.08297 + 6.41071i) q^{31} +(3.50456 - 3.50456i) q^{32} +2.57262i q^{34} +(-1.61357 - 6.31852i) q^{35} +(2.42532 - 1.76210i) q^{36} +(-0.181976 - 1.14895i) q^{37} +(-1.78369 - 0.908835i) q^{38} +(1.03037 + 3.17117i) q^{39} +(0.263237 - 4.09899i) q^{40} +(2.08980 + 2.87636i) q^{41} +(1.44582 - 0.736681i) q^{42} +(-5.07292 - 5.07292i) q^{43} +(0.834964 - 3.71273i) q^{45} +(-1.39275 - 0.452533i) q^{46} +(3.63636 + 0.575943i) q^{47} +(-2.95515 + 0.468049i) q^{48} +(1.43178 - 0.465213i) q^{49} +(-1.49151 - 1.93320i) q^{50} +(3.52805 - 4.85594i) q^{51} +(-0.806440 + 5.09166i) q^{52} +(-0.670880 - 1.31668i) q^{53} +2.61609 q^{54} +5.35716 q^{56} +(2.12044 + 4.16159i) q^{57} +(0.202033 - 1.27559i) q^{58} +(0.943564 - 1.29870i) q^{59} +(-2.86514 + 3.45420i) q^{60} +(-6.59851 + 2.14398i) q^{61} +(-3.25119 + 0.514937i) q^{62} +(4.90220 + 0.776433i) q^{63} +(-2.69314 - 0.875053i) q^{64} +(3.49920 + 5.52974i) q^{65} +(1.31471 + 1.31471i) q^{67} +(8.26845 - 4.21298i) q^{68} +(2.00829 + 2.76417i) q^{69} +(2.39155 - 2.10291i) q^{70} +(0.887847 + 2.73251i) q^{71} +(2.78541 + 1.41924i) q^{72} +(2.31553 + 14.6197i) q^{73} +(0.459581 - 0.333905i) q^{74} +(0.164135 + 5.69444i) q^{75} +7.22113i q^{76} +(-1.15138 + 1.15138i) q^{78} +(-4.71123 + 14.4997i) q^{79} +(-5.39204 + 2.32503i) q^{80} +(-0.807503 - 0.586685i) q^{81} +(-0.788233 + 1.54699i) q^{82} +(3.03387 - 5.95431i) q^{83} +(-4.73540 - 3.44047i) q^{84} +(4.35068 - 10.9470i) q^{85} +(1.08262 - 3.33197i) q^{86} +(-2.13066 + 2.13066i) q^{87} -11.1726i q^{89} +(1.80057 - 0.459814i) q^{90} +(-6.90490 + 5.01670i) q^{91} +(0.826356 + 5.21741i) q^{92} +(6.84294 + 3.48665i) q^{93} +(0.555586 + 1.70992i) q^{94} +(6.05294 + 6.88374i) q^{95} +(-3.31916 - 4.56843i) q^{96} +(8.97103 - 4.57097i) q^{97} +(0.519848 + 0.519848i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{3} - 2 q^{5} - 20 q^{7} + 20 q^{8} + 12 q^{12} + 20 q^{13} + 4 q^{15} + 12 q^{16} - 30 q^{18} + 16 q^{20} - 24 q^{23} - 24 q^{25} - 20 q^{26} + 24 q^{27} + 20 q^{28} - 40 q^{30} + 32 q^{31}+ \cdots - 38 q^{97}+O(q^{100}) $ 32 * q + 6 * q^3 - 2 * q^5 - 20 * q^7 + 20 * q^8 + 12 * q^12 + 20 * q^13 + 4 * q^15 + 12 * q^16 - 30 * q^18 + 16 * q^20 - 24 * q^23 - 24 * q^25 - 20 * q^26 + 24 * q^27 + 20 * q^28 - 40 * q^30 + 32 * q^31 - 30 * q^35 - 36 * q^36 - 8 * q^37 + 10 * q^38 + 50 * q^40 - 20 * q^42 - 28 * q^45 - 20 * q^46 + 42 * q^47 + 26 * q^48 - 80 * q^50 + 100 * q^51 + 20 * q^52 - 34 * q^53 - 80 * q^56 + 40 * q^57 + 90 * q^58 - 86 * q^60 - 10 * q^62 + 10 * q^63 - 8 * q^67 + 70 * q^68 + 10 * q^70 - 36 * q^71 + 70 * q^72 - 30 * q^73 + 4 * q^75 + 60 * q^78 - 102 * q^80 + 8 * q^81 + 20 * q^82 + 60 * q^83 - 60 * q^85 - 80 * q^86 - 130 * q^90 - 60 * q^91 + 42 * q^92 - 8 * q^93 + 30 * q^95 - 38 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.221702	+	0.435114i	0.156767	+	0.307672i	0.956009	−	0.293337i	$-0.0947657\pi$
$2$	0.221702	+	0.435114i	0.156767	+	0.307672i	−0.799243	+	0.601009i	$0.794766\pi$
$3$	0.178235	−	1.12533i	0.102904	−	0.649712i	−0.881284	−	0.472587i	$-0.843320\pi$
$3$	0.178235	−	1.12533i	0.102904	−	0.649712i	0.984188	−	0.177125i	$-0.0566798\pi$
$4$	1.03540	−	1.42510i	0.517699	−	0.712552i
$5$	−0.207538	−	2.22642i	−0.0928139	−	0.995683i
$5$	−0.207538	−	2.22642i	−0.0928139	−	0.995683i
$6$	0.529164	−	0.171936i	0.216030	−	0.0701924i
$7$	2.88051	−	0.456227i	1.08873	−	0.172438i	0.413835	−	0.910352i	$-0.364189\pi$
$7$	2.88051	−	0.456227i	1.08873	−	0.172438i	0.674894	+	0.737914i	$0.264189\pi$
$8$	1.81429	+	0.287355i	0.641447	+	0.101595i
$9$	1.61856	+	0.525902i	0.539520	+	0.175301i
$10$	0.922733	−	0.583903i	0.291794	−	0.184646i
$11$		0			0
$11$		0			0
$12$	−1.41917	−	1.41917i	−0.409680	−	0.409680i
$13$	−2.60754	+	1.32861i	−0.723203	+	0.368490i	−0.776524	−	0.630087i	$-0.783019\pi$
$13$	−2.60754	+	1.32861i	−0.723203	+	0.368490i	0.0533216	+	0.998577i	$0.483019\pi$
$14$	0.837124	+	1.15220i	0.223731	+	0.307939i
$15$	−2.54245	−	0.163276i	−0.656459	−	0.0421578i
$16$	−0.811484	−	2.49749i	−0.202871	−	0.624373i
$17$	4.69392	+	2.39167i	1.13844	+	0.580065i	0.918489	−	0.395446i	$-0.129410\pi$
$17$	4.69392	+	2.39167i	1.13844	+	0.580065i	0.219952	+	0.975511i	$0.429410\pi$
$18$	0.130010	+	0.820851i	0.0306437	+	0.193476i
$19$	−3.31646	+	2.40955i	−0.760847	+	0.552788i	−0.899170	−	0.437599i	$-0.855829\pi$
$19$	−3.31646	+	2.40955i	−0.760847	+	0.552788i	0.138323	+	0.990387i	$0.455829\pi$
$20$	−3.38776	−	2.00946i	−0.757526	−	0.449330i
$21$		−	3.32285i		−	0.725105i
$22$		0			0
$23$	−2.12046	+	2.12046i	−0.442147	+	0.442147i	−0.892733	−	0.450586i	$-0.851215\pi$
$23$	−2.12046	+	2.12046i	−0.442147	+	0.442147i	0.450586	+	0.892733i	$0.351215\pi$
$24$	0.646740	−	1.99046i	0.132015	−	0.406301i
$25$	−4.91386	+	0.924132i	−0.982771	+	0.184826i
$26$	−1.15619	−	0.840024i	−0.226748	−	0.164742i
$27$	2.43208	−	4.77322i	0.468054	−	0.918607i
$28$	2.33230	−	4.57740i	0.440763	−	0.865047i
$29$	−2.13957	−	1.55449i	−0.397307	−	0.288661i	0.371136	−	0.928579i	$-0.378968\pi$
$29$	−2.13957	−	1.55449i	−0.397307	−	0.288661i	−0.768443	+	0.639918i	$0.778968\pi$
$30$	−0.492622	−	1.14246i	−0.0899401	−	0.208583i
$31$	−2.08297	+	6.41071i	−0.374112	+	1.15140i	0.569964	+	0.821670i	$0.306957\pi$
$31$	−2.08297	+	6.41071i	−0.374112	+	1.15140i	−0.944076	+	0.329728i	$0.893043\pi$
$32$	3.50456	−	3.50456i	0.619524	−	0.619524i
$33$		0			0
$34$			2.57262i			0.441201i
$35$	−1.61357	−	6.31852i	−0.272743	−	1.06803i
$36$	2.42532	−	1.76210i	0.404220	−	0.293683i
$37$	−0.181976	−	1.14895i	−0.0299167	−	0.188887i	0.968204	−	0.250161i	$-0.0804836\pi$
$37$	−0.181976	−	1.14895i	−0.0299167	−	0.188887i	−0.998121	+	0.0612742i	$0.980484\pi$
$38$	−1.78369	−	0.908835i	−0.289353	−	0.147433i
$39$	1.03037	+	3.17117i	0.164992	+	0.507793i
$40$	0.263237	−	4.09899i	0.0416215	−	0.648108i
$41$	2.08980	+	2.87636i	0.326372	+	0.449212i	0.940399	−	0.340073i	$-0.110452\pi$
$41$	2.08980	+	2.87636i	0.326372	+	0.449212i	−0.614028	+	0.789285i	$0.710452\pi$
$42$	1.44582	−	0.736681i	0.223094	−	0.113672i
$43$	−5.07292	−	5.07292i	−0.773613	−	0.773613i	0.205123	−	0.978736i	$-0.434241\pi$
$43$	−5.07292	−	5.07292i	−0.773613	−	0.773613i	−0.978736	+	0.205123i	$0.934241\pi$
$44$		0			0
$45$	0.834964	−	3.71273i	0.124469	−	0.553461i
$46$	−1.39275	−	0.452533i	−0.205350	−	0.0667224i
$47$	3.63636	+	0.575943i	0.530417	+	0.0840099i	0.415898	−	0.909411i	$-0.363467\pi$
$47$	3.63636	+	0.575943i	0.530417	+	0.0840099i	0.114519	+	0.993421i	$0.463467\pi$
$48$	−2.95515	+	0.468049i	−0.426539	+	0.0675571i
$49$	1.43178	−	0.465213i	0.204540	−	0.0664590i
$50$	−1.49151	−	1.93320i	−0.210932	−	0.273396i
$51$	3.52805	−	4.85594i	0.494026	−	0.679968i
$52$	−0.806440	+	5.09166i	−0.111833	+	0.706086i
$53$	−0.670880	−	1.31668i	−0.0921524	−	0.180859i	0.840330	−	0.542076i	$-0.182361\pi$
$53$	−0.670880	−	1.31668i	−0.0921524	−	0.180859i	−0.932482	+	0.361217i	$0.882361\pi$
$54$	2.61609			0.356005
$55$		0			0
$56$	5.35716			0.715881
$57$	2.12044	+	4.16159i	0.280859	+	0.551216i
$58$	0.202033	−	1.27559i	0.0265282	−	0.167493i
$59$	0.943564	−	1.29870i	0.122842	−	0.169077i	−0.743167	−	0.669106i	$-0.766677\pi$
$59$	0.943564	−	1.29870i	0.122842	−	0.169077i	0.866009	+	0.500029i	$0.166677\pi$
$60$	−2.86514	+	3.45420i	−0.369888	+	0.445936i
$61$	−6.59851	+	2.14398i	−0.844852	+	0.274509i	−0.699288	−	0.714840i	$-0.746500\pi$
$61$	−6.59851	+	2.14398i	−0.844852	+	0.274509i	−0.145564	+	0.989349i	$0.546500\pi$
$62$	−3.25119	+	0.514937i	−0.412901	+	0.0653971i
$63$	4.90220	+	0.776433i	0.617619	+	0.0978213i
$64$	−2.69314	−	0.875053i	−0.336642	−	0.109382i
$65$	3.49920	+	5.52974i	0.434023	+	0.685880i
$66$		0			0
$67$	1.31471	+	1.31471i	0.160617	+	0.160617i	0.782840	−	0.622223i	$-0.213770\pi$
$67$	1.31471	+	1.31471i	0.160617	+	0.160617i	−0.622223	+	0.782840i	$0.713770\pi$
$68$	8.26845	−	4.21298i	1.00270	−	0.510899i
$69$	2.00829	+	2.76417i	0.241770	+	0.332767i
$70$	2.39155	−	2.10291i	0.285844	−	0.251346i
$71$	0.887847	+	2.73251i	0.105368	+	0.324289i	0.989817	−	0.142348i	$-0.0454653\pi$
$71$	0.887847	+	2.73251i	0.105368	+	0.324289i	−0.884449	+	0.466638i	$0.845465\pi$
$72$	2.78541	+	1.41924i	0.328264	+	0.167259i
$73$	2.31553	+	14.6197i	0.271012	+	1.71110i	0.629025	+	0.777385i	$0.283454\pi$
$73$	2.31553	+	14.6197i	0.271012	+	1.71110i	−0.358013	+	0.933716i	$0.616546\pi$
$74$	0.459581	−	0.333905i	0.0534252	−	0.0388157i
$75$	0.164135	+	5.69444i	0.0189526	+	0.657538i
$76$			7.22113i			0.828321i
$77$		0			0
$78$	−1.15138	+	1.15138i	−0.130368	+	0.130368i
$79$	−4.71123	+	14.4997i	−0.530055	+	1.63134i	0.224043	+	0.974579i	$0.428074\pi$
$79$	−4.71123	+	14.4997i	−0.530055	+	1.63134i	−0.754098	+	0.656762i	$0.771926\pi$
$80$	−5.39204	+	2.32503i	−0.602848	+	0.259946i
$81$	−0.807503	−	0.586685i	−0.0897226	−	0.0651873i
$82$	−0.788233	+	1.54699i	−0.0870457	+	0.170837i
$83$	3.03387	−	5.95431i	0.333011	−	0.653571i	−0.662412	−	0.749140i	$-0.730467\pi$
$83$	3.03387	−	5.95431i	0.333011	−	0.653571i	0.995423	+	0.0955691i	$0.0304671\pi$
$84$	−4.73540	−	3.44047i	−0.516675	−	0.375386i
$85$	4.35068	−	10.9470i	0.471898	−	1.18737i
$86$	1.08262	−	3.33197i	0.116742	−	0.359296i
$87$	−2.13066	+	2.13066i	−0.228431	+	0.228431i
$88$		0			0
$89$		−	11.1726i		−	1.18429i	−0.805830	−	0.592147i	$-0.798281\pi$
$89$		−	11.1726i		−	1.18429i	0.805830	−	0.592147i	$-0.201719\pi$
$90$	1.80057	−	0.459814i	0.189797	−	0.0484687i
$91$	−6.90490	+	5.01670i	−0.723830	+	0.525894i
$92$	0.826356	+	5.21741i	0.0861536	+	0.543952i
$93$	6.84294	+	3.48665i	0.709580	+	0.361549i
$94$	0.555586	+	1.70992i	0.0573043	+	0.176364i
$95$	6.05294	+	6.88374i	0.621019	+	0.706257i
$96$	−3.31916	−	4.56843i	−0.338761	−	0.466264i
$97$	8.97103	−	4.57097i	0.910871	−	0.464112i	0.0652335	−	0.997870i	$-0.479221\pi$
$97$	8.97103	−	4.57097i	0.910871	−	0.464112i	0.845637	+	0.533758i	$0.179221\pi$
$98$	0.519848	+	0.519848i	0.0525126	+	0.0525126i
$99$		0			0
$100$	−3.77081	+	7.95960i	−0.377081	+	0.795960i
$101$	−1.81570	−	0.589955i	−0.180668	−	0.0587027i	0.217286	−	0.976108i	$-0.430280\pi$
$101$	−1.81570	−	0.589955i	−0.180668	−	0.0587027i	−0.397954	+	0.917405i	$0.630280\pi$
$102$	2.89506	+	0.458533i	0.286654	+	0.0454015i
$103$	6.09534	−	0.965408i	0.600592	−	0.0951244i	0.151267	−	0.988493i	$-0.451665\pi$
$103$	6.09534	−	0.965408i	0.600592	−	0.0951244i	0.449325	+	0.893368i	$0.351665\pi$
$104$	−5.11261	+	1.66119i	−0.501333	+	0.162893i
$105$	−7.39804	+	0.689618i	−0.721975	+	0.0672998i
$106$	0.424169	−	0.583818i	0.0411989	−	0.0567054i
$107$	0.0681317	−	0.430167i	0.00658654	−	0.0415858i	−0.984176	−	0.177193i	$-0.943298\pi$
$107$	0.0681317	−	0.430167i	0.00658654	−	0.0415858i	0.990763	+	0.135607i	$0.0432984\pi$
$108$	−4.28417	−	8.40815i	−0.412244	−	0.809075i
$109$	−9.46672			−0.906748			−0.453374	−	0.891320i	$-0.649780\pi$
$109$	−9.46672			−0.906748			−0.453374	+	0.891320i	$0.649780\pi$
$110$		0			0
$111$	−1.32539			−0.125801
$112$	−3.47691	−	6.82382i	−0.328537	−	0.644790i
$113$	3.17038	−	20.0170i	0.298244	−	1.88304i	−0.149322	−	0.988789i	$-0.547709\pi$
$113$	3.17038	−	20.0170i	0.298244	−	1.88304i	0.447566	−	0.894251i	$-0.352291\pi$
$114$	−1.34066	+	1.84526i	−0.125564	+	0.172825i
$115$	5.16111	+	4.28096i	0.481276	+	0.399202i
$116$	−4.43060	+	1.43959i	−0.411371	+	0.133663i
$117$	−4.91919	+	0.779122i	−0.454779	+	0.0720299i
$118$	0.774274	+	0.122633i	0.0712777	+	0.0112893i
$119$	14.6120	+	4.74773i	1.33948	+	0.435223i
$120$	−4.56582	−	1.02682i	−0.416800	−	0.0937351i
$121$		0			0
$122$	−2.39578	−	2.39578i	−0.216903	−	0.216903i
$123$	3.60934	−	1.83905i	0.325444	−	0.165822i
$124$	6.97923	+	9.60608i	0.626753	+	0.862652i
$125$	3.07732	+	10.7485i	0.275243	+	0.961375i
$126$	0.748989	+	2.30515i	0.0667253	+	0.205359i
$127$	−8.40191	−	4.28099i	−0.745549	−	0.379876i	0.0395736	−	0.999217i	$-0.487400\pi$
$127$	−8.40191	−	4.28099i	−0.745549	−	0.379876i	−0.785122	+	0.619341i	$0.787400\pi$
$128$	−1.76696	−	11.1562i	−0.156179	−	0.986075i
$129$	−6.61291	+	4.80456i	−0.582234	+	0.423018i
$130$	−1.63029	+	2.74850i	−0.142986	+	0.241060i
$131$			7.51676i			0.656743i	0.944549	+	0.328371i	$0.106500\pi$
$131$			7.51676i			0.656743i	−0.944549	+	0.328371i	$0.893500\pi$
$132$		0			0
$133$	−8.45377	+	8.45377i	−0.733035	+	0.733035i
$134$	−0.280575	+	0.863521i	−0.0242380	+	0.0745968i
$135$	−11.1319	−	4.42419i	−0.958084	−	0.380774i
$136$	7.82885	+	5.68799i	0.671318	+	0.487741i
$137$	−6.97753	+	13.6942i	−0.596131	+	1.16997i	0.374009	+	0.927425i	$0.377983\pi$
$137$	−6.97753	+	13.6942i	−0.596131	+	1.16997i	−0.970140	+	0.242547i	$0.922017\pi$
$138$	−0.757489	+	1.48666i	−0.0644818	+	0.126553i
$139$	−3.36744	−	2.44659i	−0.285623	−	0.207517i	0.435743	−	0.900071i	$-0.356486\pi$
$139$	−3.36744	−	2.44659i	−0.285623	−	0.207517i	−0.721366	+	0.692554i	$0.756486\pi$
$140$	−10.6752	−	4.24269i	−0.902222	−	0.358572i
$141$	1.29626	−	3.98947i	0.109164	−	0.335974i
$142$	−0.992116	+	0.992116i	−0.0832565	+	0.0832565i
$143$		0			0
$144$		−	4.46910i		−	0.372425i
$145$	−3.01689	+	5.08618i	−0.250539	+	0.422384i
$146$	−5.84786	+	4.24872i	−0.483972	+	0.351626i
$147$	−0.268327	−	1.69415i	−0.0221312	−	0.139731i
$148$	−1.82580	−	0.930290i	−0.150080	−	0.0764693i
$149$	5.55533	+	17.0976i	0.455111	+	1.40069i	0.871005	+	0.491273i	$0.163468\pi$
$149$	5.55533	+	17.0976i	0.455111	+	1.40069i	−0.415895	+	0.909413i	$0.636532\pi$
$150$	−2.44134	+	1.33388i	−0.199335	+	0.108911i
$151$	−10.4580	−	14.3942i	−0.851058	−	1.17138i	−0.983629	−	0.180207i	$-0.942323\pi$
$151$	−10.4580	−	14.3942i	−0.851058	−	1.17138i	0.132571	−	0.991173i	$-0.457677\pi$
$152$	−6.70939	+	3.41861i	−0.544204	+	0.277286i
$153$	6.33960	+	6.33960i	0.512526	+	0.512526i
$154$		0			0
$155$	14.7052	+	3.30708i	1.18115	+	0.265631i
$156$	5.58609	+	1.81503i	0.447245	+	0.145319i
$157$	21.2006	+	3.35784i	1.69199	+	0.267985i	0.926727	−	0.375735i	$-0.122610\pi$
$157$	21.2006	+	3.35784i	1.69199	+	0.267985i	0.765261	+	0.643720i	$0.222610\pi$
$158$	−7.35350	+	1.16468i	−0.585013	+	0.0926569i
$159$	−1.60127	+	0.520286i	−0.126989	+	0.0412613i
$160$	−8.52993	−	7.07527i	−0.674350	−	0.559349i
$161$	−5.14060	+	7.07543i	−0.405136	+	0.557622i
$162$	0.0762502	−	0.481425i	0.00599078	−	0.0378243i
$163$	−4.73286	−	9.28876i	−0.370706	−	0.727552i	0.628010	−	0.778205i	$-0.283870\pi$
$163$	−4.73286	−	9.28876i	−0.370706	−	0.727552i	−0.998716	+	0.0506534i	$0.983870\pi$
$164$	6.26288			0.489049
$165$		0			0
$166$	3.26342			0.253290
$167$	5.12686	+	10.0620i	0.396728	+	0.778623i	0.999819	−	0.0190498i	$-0.00606412\pi$
$167$	5.12686	+	10.0620i	0.396728	+	0.778623i	−0.603090	+	0.797673i	$0.706064\pi$
$168$	0.954836	−	6.02860i	0.0736672	−	0.465117i
$169$	−2.60712	+	3.58840i	−0.200548	+	0.276031i
$170$	5.72773	−	0.533918i	0.439297	−	0.0409496i
$171$	−6.63507	+	2.15586i	−0.507396	+	0.164863i
$172$	−12.4819	+	1.97694i	−0.951738	+	0.150741i
$173$	13.0397	+	2.06528i	0.991387	+	0.157020i	0.631000	−	0.775783i	$-0.282645\pi$
$173$	13.0397	+	2.06528i	0.991387	+	0.157020i	0.360387	+	0.932803i	$0.382645\pi$
$174$	−1.39945	−	0.454709i	−0.106092	−	0.0344714i
$175$	−13.7328	+	4.90381i	−1.03810	+	0.370693i
$176$		0			0
$177$	−1.29330	−	1.29330i	−0.0972104	−	0.0972104i
$178$	4.86135	−	2.47698i	0.364374	−	0.185658i
$179$	−1.30884	−	1.80147i	−0.0978276	−	0.134648i	0.757297	−	0.653071i	$-0.226520\pi$
$179$	−1.30884	−	1.80147i	−0.0978276	−	0.134648i	−0.855125	+	0.518422i	$0.826520\pi$
$180$	−4.42651	−	5.03406i	−0.329932	−	0.375217i
$181$	1.33951	+	4.12258i	0.0995647	+	0.306429i	0.988416	−	0.151766i	$-0.0484961\pi$
$181$	1.33951	+	4.12258i	0.0995647	+	0.306429i	−0.888852	+	0.458195i	$0.848496\pi$
$182$	−3.71366	−	1.89221i	−0.275275	−	0.140260i
$183$	1.23661	+	7.80766i	0.0914130	+	0.577159i
$184$	−4.45646	+	3.23780i	−0.328534	+	0.238694i
$185$	−2.52028	+	0.643607i	−0.185295	+	0.0473189i
$186$			3.75045i			0.274996i
$187$		0			0
$188$	4.58586	−	4.58586i	0.334458	−	0.334458i
$189$	4.82794	−	14.8589i	0.351181	−	1.08082i
$190$	−1.65326	+	4.15985i	−0.119940	+	0.301788i
$191$	3.29900	+	2.39686i	0.238707	+	0.173431i	0.700707	−	0.713449i	$-0.252868\pi$
$191$	3.29900	+	2.39686i	0.238707	+	0.173431i	−0.462000	+	0.886880i	$0.652868\pi$
$192$	−1.46474	+	2.87471i	−0.105708	+	0.207465i
$193$	9.48874	−	18.6227i	0.683015	−	1.34049i	−0.245573	−	0.969378i	$-0.578976\pi$
$193$	9.48874	−	18.6227i	0.683015	−	1.34049i	0.928588	−	0.371113i	$-0.121024\pi$
$194$	3.97778	+	2.89003i	0.285588	+	0.207492i
$195$	6.84649	−	2.95218i	0.490287	−	0.211410i
$196$	0.819484	−	2.52211i	0.0585346	−	0.180151i
$197$	−0.213782	+	0.213782i	−0.0152313	+	0.0152313i	−0.714681	−	0.699450i	$-0.753428\pi$
$197$	−0.213782	+	0.213782i	−0.0152313	+	0.0152313i	0.699450	+	0.714681i	$0.253428\pi$
$198$		0			0
$199$			11.0815i			0.785549i	0.919635	+	0.392775i	$0.128485\pi$
$199$			11.0815i			0.785549i	−0.919635	+	0.392775i	$0.871515\pi$
$200$	−9.18069	+	0.264621i	−0.649173	+	0.0187115i
$201$	1.71381	−	1.24516i	0.120883	−	0.0878267i
$202$	−0.145845	−	0.920828i	−0.0102616	−	0.0647892i
$203$	−6.87223	−	3.50158i	−0.482336	−	0.245762i
$204$	−3.26729	−	10.0557i	−0.228756	−	0.704038i
$205$	5.97026	−	5.24971i	0.416981	−	0.366656i
$206$	1.77141	+	2.43814i	0.123420	+	0.169873i
$207$	−4.54726	+	2.31694i	−0.316056	+	0.161039i
$208$	5.43417	+	5.43417i	0.376792	+	0.376792i
$209$		0			0
$210$	−1.94022	−	3.06610i	−0.133888	−	0.211581i
$211$	−8.42206	−	2.73649i	−0.579799	−	0.188388i	0.00441172	−	0.999990i	$-0.498596\pi$
$211$	−8.42206	−	2.73649i	−0.579799	−	0.188388i	−0.584210	+	0.811602i	$0.698596\pi$
$212$	−2.57103	−	0.407211i	−0.176579	−	0.0279673i
$213$	3.23323	−	0.512094i	0.221538	−	0.0350881i
$214$	0.202276	−	0.0657236i	0.0138273	−	0.00449277i
$215$	−10.2416	+	12.3473i	−0.698472	+	0.842076i
$216$	5.78409	−	7.96112i	0.393558	−	0.541686i
$217$	−3.07526	+	19.4164i	−0.208762	+	1.31807i
$218$	−2.09879	−	4.11910i	−0.142148	−	0.278981i
$219$	16.8647			1.13961
$220$		0			0
$221$	−15.4172			−1.03707
$222$	−0.293842	−	0.576696i	−0.0197214	−	0.0387053i
$223$	−0.967112	+	6.10610i	−0.0647626	+	0.408895i	0.933916	+	0.357494i	$0.116369\pi$
$223$	−0.967112	+	6.10610i	−0.0647626	+	0.408895i	−0.998678	+	0.0514011i	$0.983631\pi$
$224$	8.49602	−	11.6938i	0.567664	−	0.781323i
$225$	−8.43937	−	1.08844i	−0.562625	−	0.0725628i
$226$	9.41254	−	3.05832i	0.626113	−	0.203436i
$227$	3.27588	−	0.518849i	0.217428	−	0.0344372i	−0.0467700	−	0.998906i	$-0.514893\pi$
$227$	3.27588	−	0.518849i	0.217428	−	0.0344372i	0.264198	+	0.964468i	$0.414893\pi$
$228$	8.12619	+	1.28706i	0.538170	+	0.0852377i
$229$	5.07862	+	1.65014i	0.335604	+	0.109044i	0.471971	−	0.881614i	$-0.343543\pi$
$229$	5.07862	+	1.65014i	0.335604	+	0.109044i	−0.136367	+	0.990658i	$0.543543\pi$
$230$	−0.718477	+	3.19477i	−0.0473750	+	0.210657i
$231$		0			0
$232$	−3.43509	−	3.43509i	−0.225525	−	0.225525i
$233$	3.93669	−	2.00585i	0.257901	−	0.131407i	−0.320260	−	0.947330i	$-0.603770\pi$
$233$	3.93669	−	2.00585i	0.257901	−	0.131407i	0.578162	+	0.815922i	$0.303770\pi$
$234$	−1.42960	−	1.96767i	−0.0934557	−	0.128631i
$235$	0.527605	−	8.21558i	0.0344171	−	0.535925i
$236$	−0.873824	−	2.68935i	−0.0568811	−	0.175062i
$237$	15.4773	+	7.88607i	1.00536	+	0.512255i
$238$	1.17370	+	7.41046i	0.0760798	+	0.480349i
$239$	8.45656	−	6.14405i	0.547009	−	0.397426i	−0.279672	−	0.960096i	$-0.590226\pi$
$239$	8.45656	−	6.14405i	0.547009	−	0.397426i	0.826682	+	0.562670i	$0.190226\pi$
$240$	1.65538	+	6.48225i	0.106854	+	0.418427i
$241$		−	27.8579i		−	1.79449i	−0.441536	−	0.897243i	$-0.645566\pi$
$241$		−	27.8579i		−	1.79449i	0.441536	−	0.897243i	$-0.354434\pi$
$242$		0			0
$243$	10.5600	−	10.5600i	0.677425	−	0.677425i
$244$	−3.77668	+	11.6234i	−0.241777	+	0.744114i
$245$	−1.33291	−	3.09119i	−0.0851563	−	0.197489i
$246$	1.60039	+	1.16275i	0.102037	+	0.0741345i
$247$	5.44646	−	10.6893i	0.346550	−	0.680142i
$248$	−5.62125	+	11.0323i	−0.356949	+	0.700553i
$249$	−6.15985	−	4.47539i	−0.390365	−	0.283616i
$250$	−3.99457	+	3.72194i	−0.252639	+	0.235396i
$251$	−3.07357	+	9.45946i	−0.194002	+	0.597076i	0.805985	+	0.591936i	$0.201636\pi$
$251$	−3.07357	+	9.45946i	−0.194002	+	0.597076i	−0.999987	+	0.00514015i	$0.998364\pi$
$252$	6.18223	−	6.18223i	0.389444	−	0.389444i
$253$		0			0
$254$		−	4.60489i		−	0.288936i
$255$	−11.5436	−	6.84711i	−0.722886	−	0.428783i
$256$	−0.119374	+	0.0867302i	−0.00746087	+	0.00542064i
$257$	−0.663355	−	4.18826i	−0.0413790	−	0.261257i	0.958323	−	0.285689i	$-0.0922223\pi$
$257$	−0.663355	−	4.18826i	−0.0413790	−	0.261257i	−0.999701	+	0.0244320i	$0.992222\pi$
$258$	−3.55662	−	1.81219i	−0.221426	−	0.112822i
$259$	−1.04837	−	3.22655i	−0.0651425	−	0.200488i
$260$	11.5035	+	0.738757i	0.713418	+	0.0458157i
$261$	−2.64551	−	3.64123i	−0.163753	−	0.225386i
$262$	−3.27065	+	1.66648i	−0.202061	+	0.102955i
$263$	−16.1830	−	16.1830i	−0.997884	−	0.997884i	0.00211364	−	0.999998i	$-0.499327\pi$
$263$	−16.1830	−	16.1830i	−0.997884	−	0.997884i	−0.999998	+	0.00211364i	$0.999327\pi$
$264$		0			0
$265$	−2.79223	+	1.76692i	−0.171526	+	0.108541i
$266$	−5.55257	−	1.80414i	−0.340450	−	0.110619i
$267$	−12.5729	−	1.99135i	−0.769450	−	0.121869i
$268$	3.23484	−	0.512349i	0.197599	−	0.0312967i
$269$	21.7521	−	7.06768i	1.32625	−	0.430924i	0.441611	−	0.897206i	$-0.354407\pi$
$269$	21.7521	−	7.06768i	1.32625	−	0.430924i	0.884636	+	0.466283i	$0.154407\pi$
$270$	−0.542939	−	5.82451i	−0.0330422	−	0.354468i
$271$	0.817223	−	1.12481i	0.0496428	−	0.0683274i	−0.783474	−	0.621425i	$-0.786554\pi$
$271$	0.817223	−	1.12481i	0.0496428	−	0.0683274i	0.833117	+	0.553097i	$0.186554\pi$
$272$	2.16414	−	13.6638i	0.131220	−	0.828490i
$273$	4.41477	+	8.66448i	0.267194	+	0.524398i
$274$	−7.50545			−0.453421
$275$		0			0
$276$	6.01861			0.362278
$277$	6.47199	+	12.7020i	0.388864	+	0.763189i	0.999589	−	0.0286534i	$-0.00912190\pi$
$277$	6.47199	+	12.7020i	0.388864	+	0.763189i	−0.610725	+	0.791843i	$0.709122\pi$
$278$	0.317978	−	2.00763i	0.0190711	−	0.120410i
$279$	−6.74281	+	9.28068i	−0.403682	+	0.555620i
$280$	−1.11182	−	11.9273i	−0.0664437	−	0.712791i
$281$	24.1347	−	7.84184i	1.43976	−	0.467805i	0.517935	−	0.855420i	$-0.326701\pi$
$281$	24.1347	−	7.84184i	1.43976	−	0.467805i	0.921821	+	0.387615i	$0.126701\pi$
$282$	2.02325	−	0.320452i	0.120483	−	0.0190826i
$283$	−7.31948	−	1.15929i	−0.435098	−	0.0689128i	−0.0649564	−	0.997888i	$-0.520691\pi$
$283$	−7.31948	−	1.15929i	−0.435098	−	0.0689128i	−0.370142	+	0.928975i	$0.620691\pi$
$284$	4.81338	+	1.56396i	0.285622	+	0.0928042i
$285$	8.82536	−	5.58466i	0.522769	−	0.330807i
$286$		0			0
$287$	7.33195	+	7.33195i	0.432791	+	0.432791i
$288$	7.51539	−	3.82928i	0.442848	−	0.225643i
$289$	6.32041	+	8.69930i	0.371789	+	0.511724i
$290$	−2.88191	−	0.185077i	−0.169232	−	0.0108681i
$291$	−3.54491	−	10.9101i	−0.207807	−	0.639563i
$292$	23.2320	+	11.8373i	1.35955	+	0.692726i
$293$	−2.29605	−	14.4967i	−0.134137	−	0.846906i	−0.959378	−	0.282125i	$-0.908961\pi$
$293$	−2.29605	−	14.4967i	−0.134137	−	0.846906i	0.825241	−	0.564781i	$-0.191039\pi$
$294$	0.677659	−	0.492348i	0.0395219	−	0.0287143i
$295$	−3.08728	−	1.83124i	−0.179749	−	0.106619i
$296$		−	2.13682i		−	0.124200i
$297$		0			0
$298$	−6.20775	+	6.20775i	−0.359606	+	0.359606i
$299$	2.71194	−	8.34648i	0.156835	−	0.482689i
$300$	8.28512	+	5.66211i	0.478341	+	0.326902i
$301$	−16.9270	−	12.2982i	−0.975655	−	0.708855i
$302$	3.94455	−	7.74161i	0.226983	−	0.445480i
$303$	−0.987518	+	1.93811i	−0.0567314	+	0.111342i
$304$	8.70907	+	6.32751i	0.499499	+	0.362908i
$305$	6.14284	+	14.2461i	0.351738	+	0.815727i
$306$	−1.35295	+	4.16395i	−0.0773429	+	0.238037i
$307$	0.874954	−	0.874954i	0.0499363	−	0.0499363i	−0.681698	−	0.731634i	$-0.738758\pi$
$307$	0.874954	−	0.874954i	0.0499363	−	0.0499363i	0.731634	+	0.681698i	$0.238758\pi$
$308$		0			0
$309$		−	7.03137i		−	0.400001i
$310$	1.82121	+	7.13162i	0.103438	+	0.405049i
$311$	−11.4450	+	8.31532i	−0.648989	+	0.471518i	−0.862927	−	0.505329i	$-0.831371\pi$
$311$	−11.4450	+	8.31532i	−0.648989	+	0.471518i	0.213937	+	0.976847i	$0.431371\pi$
$312$	0.958144	+	6.04948i	0.0542442	+	0.342485i
$313$	−0.659031	−	0.335793i	−0.0372506	−	0.0189802i	0.435266	−	0.900302i	$-0.356654\pi$
$313$	−0.659031	−	0.335793i	−0.0372506	−	0.0189802i	−0.472517	+	0.881322i	$0.656654\pi$
$314$	3.23915	+	9.96909i	0.182796	+	0.562588i
$315$	0.711268	−	11.0755i	0.0400754	−	0.624033i
$316$	15.7855	+	21.7269i	0.888006	+	1.22224i
$317$	15.2060	−	7.74784i	0.854054	−	0.435162i	0.0285725	−	0.999592i	$-0.490904\pi$
$317$	15.2060	−	7.74784i	0.854054	−	0.435162i	0.825481	+	0.564430i	$0.190904\pi$
$318$	−0.581389	−	0.581389i	−0.0326027	−	0.0326027i
$319$		0			0
$320$	−1.38930	+	6.17765i	−0.0776644	+	0.345341i
$321$	−0.471938	−	0.153342i	−0.0263410	−	0.00855871i
$322$	−4.21829	−	0.668112i	−0.235076	−	0.0372324i
$323$	−21.3300	+	3.37834i	−1.18683	+	0.187976i
$324$	−1.67217	+	0.543322i	−0.0928986	+	0.0301846i
$325$	11.5853	−	8.93832i	0.642636	−	0.495809i
$326$	2.99238	−	4.11866i	0.165733	−	0.228112i
$327$	−1.68731	+	10.6532i	−0.0933082	+	0.589125i
$328$	2.96496	+	5.81905i	0.163712	+	0.321304i
$329$	10.7373			0.591967
$330$		0			0
$331$	−14.9189			−0.820016			−0.410008	−	0.912082i	$-0.634474\pi$
$331$	−14.9189			−0.820016			−0.410008	+	0.912082i	$0.634474\pi$
$332$	−5.34424	−	10.4887i	−0.293303	−	0.575640i
$333$	0.309697	−	1.95535i	0.0169713	−	0.107153i
$334$	−3.24149	+	4.46153i	−0.177367	+	0.244124i
$335$	2.65424	−	3.19994i	0.145016	−	0.174831i
$336$	−8.29879	+	2.69644i	−0.452736	+	0.147103i
$337$	9.32134	−	1.47636i	0.507766	−	0.0804222i	0.102705	−	0.994712i	$-0.467250\pi$
$337$	9.32134	−	1.47636i	0.507766	−	0.0804222i	0.405061	+	0.914290i	$0.367250\pi$
$338$	−2.13936	−	0.338842i	−0.116366	−	0.0184306i
$339$	−21.9607	−	7.13547i	−1.19274	−	0.387546i
$340$	−11.0959	−	17.5346i	−0.601758	−	0.950950i
$341$		0			0
$342$	−2.40905	−	2.40905i	−0.130267	−	0.130267i
$343$	−14.2778	+	7.27490i	−0.770928	+	0.392808i
$344$	−7.74600	−	10.6615i	−0.417636	−	0.574827i
$345$	5.73740	−	5.04496i	0.308891	−	0.271612i
$346$	1.99228	+	6.13161i	0.107106	+	0.329637i
$347$	−17.1425	−	8.73452i	−0.920255	−	0.468894i	−0.0713577	−	0.997451i	$-0.522733\pi$
$347$	−17.1425	−	8.73452i	−0.920255	−	0.468894i	−0.848898	+	0.528557i	$0.822733\pi$
$348$	0.830330	+	5.24250i	0.0445104	+	0.281027i
$349$	−12.0325	+	8.74209i	−0.644082	+	0.467953i	−0.861250	−	0.508181i	$-0.830318\pi$
$349$	−12.0325	+	8.74209i	−0.644082	+	0.467953i	0.217168	+	0.976134i	$0.430318\pi$
$350$	−5.17829	−	4.88814i	−0.276791	−	0.261282i
$351$			15.6777i			0.836813i
$352$		0			0
$353$	1.78406	−	1.78406i	0.0949560	−	0.0949560i	−0.658033	−	0.752989i	$-0.728611\pi$
$353$	1.78406	−	1.78406i	0.0949560	−	0.0949560i	0.752989	+	0.658033i	$0.228611\pi$
$354$	0.276006	−	0.849460i	0.0146696	−	0.0451483i
$355$	5.89944	−	2.54382i	0.313110	−	0.135012i
$356$	−15.9221	−	11.5681i	−0.843870	−	0.613108i
$357$	7.94716	−	15.5972i	0.420608	−	0.825490i
$358$	0.493672	−	0.968885i	0.0260914	−	0.0512072i
$359$	6.87015	+	4.99146i	0.362593	+	0.263439i	0.754133	−	0.656722i	$-0.228058\pi$
$359$	6.87015	+	4.99146i	0.362593	+	0.263439i	−0.391540	+	0.920161i	$0.628058\pi$
$360$	2.58173	−	6.49603i	0.136069	−	0.342371i
$361$	−0.678357	+	2.08777i	−0.0357030	+	0.109883i
$362$	−1.49682	+	1.49682i	−0.0786711	+	0.0786711i
$363$		0			0
$364$			15.0345i			0.788021i
$365$	32.0689	−	8.18946i	1.67856	−	0.428656i
$366$	−3.12306	+	2.26904i	−0.163245	+	0.118604i
$367$	−3.32102	−	20.9681i	−0.173356	−	1.09453i	−0.908889	−	0.417038i	$-0.863068\pi$
$367$	−3.32102	−	20.9681i	−0.173356	−	1.09453i	0.735533	−	0.677489i	$-0.236932\pi$
$368$	7.01656	+	3.57512i	0.365764	+	0.186366i
$369$	1.86978	+	5.75459i	0.0973368	+	0.299572i
$370$	−0.838793	−	0.953921i	−0.0436068	−	0.0495920i
$371$	−2.53318	−	3.48662i	−0.131516	−	0.181016i
$372$	12.0540	−	6.14182i	0.624971	−	0.318439i
$373$	−2.57445	−	2.57445i	−0.133300	−	0.133300i	0.637309	−	0.770609i	$-0.280048\pi$
$373$	−2.57445	−	2.57445i	−0.133300	−	0.133300i	−0.770609	+	0.637309i	$0.780048\pi$
$374$		0			0
$375$	12.6441	−	1.54725i	0.652940	−	0.0798995i
$376$	6.43190	+	2.08985i	0.331700	+	0.107776i
$377$	7.64432	+	1.21074i	0.393702	+	0.0623563i
$378$	7.53567	−	1.19353i	0.387593	−	0.0613887i
$379$	−15.7712	+	5.12437i	−0.810112	+	0.263221i	−0.684645	−	0.728877i	$-0.740043\pi$
$379$	−15.7712	+	5.12437i	−0.810112	+	0.263221i	−0.125467	+	0.992098i	$0.540043\pi$
$380$	16.0772	−	1.49866i	0.824745	−	0.0768796i
$381$	−6.31506	+	8.69193i	−0.323530	+	0.445301i
$382$	−0.311515	+	1.96683i	−0.0159385	+	0.100632i
$383$	5.14840	+	10.1043i	0.263071	+	0.516306i	0.984325	−	0.176365i	$-0.0564338\pi$
$383$	5.14840	+	10.1043i	0.263071	+	0.516306i	−0.721254	+	0.692671i	$0.756434\pi$
$384$	−12.8694			−0.656736
$385$		0			0
$386$	10.2067			0.519505
$387$	−5.54297	−	10.8787i	−0.281765	−	0.552995i
$388$	2.77449	−	17.5174i	0.140853	−	0.889312i
$389$	−0.480555	+	0.661427i	−0.0243651	+	0.0335357i	−0.821026	−	0.570891i	$-0.806598\pi$
$389$	−0.480555	+	0.661427i	−0.0243651	+	0.0335357i	0.796661	+	0.604427i	$0.206598\pi$
$390$	2.80241	+	2.32450i	0.141906	+	0.117706i
$391$	−15.0247	+	4.88183i	−0.759833	+	0.246885i
$392$	2.73134	−	0.432601i	0.137953	−	0.0218497i
$393$	8.45887	+	1.33975i	0.426694	+	0.0675816i
$394$	−0.140415	−	0.0456237i	−0.00707402	−	0.00229849i
$395$	33.2601	+	7.47992i	1.67350	+	0.376356i
$396$		0			0
$397$	11.8504	+	11.8504i	0.594752	+	0.594752i	0.938911	−	0.344159i	$-0.111836\pi$
$397$	11.8504	+	11.8504i	0.594752	+	0.594752i	−0.344159	+	0.938911i	$0.611836\pi$
$398$	−4.82173	+	2.45679i	−0.241691	+	0.123148i
$399$	8.00656	+	11.0201i	0.400829	+	0.551694i
$400$	6.29553	+	11.5224i	0.314776	+	0.576120i
$401$	−8.79392	−	27.0649i	−0.439148	−	1.35156i	−0.888776	−	0.458342i	$-0.848444\pi$
$401$	−8.79392	−	27.0649i	−0.439148	−	1.35156i	0.449629	−	0.893216i	$-0.351556\pi$
$402$	0.921741	+	0.469651i	0.0459723	+	0.0234240i
$403$	−3.08591	−	19.4837i	−0.153720	−	0.970551i
$404$	−2.72071	+	1.97671i	−0.135361	+	0.0983452i
$405$	−1.13862	+	1.91960i	−0.0565784	+	0.0953856i
$406$		−	3.76651i		−	0.186929i
$407$		0			0
$408$	7.79627	−	7.79627i	0.385973	−	0.385973i
$409$	−0.748644	+	2.30409i	−0.0370181	+	0.113930i	−0.967858	−	0.251497i	$-0.919077\pi$
$409$	−0.748644	+	2.30409i	−0.0370181	+	0.113930i	0.930840	+	0.365427i	$0.119077\pi$
$410$	3.60784	+	1.43387i	0.178178	+	0.0708140i
$411$	14.1669	+	10.2928i	0.698801	+	0.507708i
$412$	4.93530	−	9.68608i	0.243145	−	0.477199i
$413$	2.12544	−	4.17141i	0.104586	−	0.205262i
$414$	−2.01627	−	1.46490i	−0.0990941	−	0.0719961i
$415$	−13.8864	−	5.51892i	−0.681658	−	0.270913i
$416$	−4.48210	+	13.7945i	−0.219753	+	0.676330i
$417$	−3.35343	+	3.35343i	−0.164218	+	0.164218i
$418$		0			0
$419$		−	16.4371i		−	0.803006i	−0.915858	−	0.401503i	$-0.868488\pi$
$419$		−	16.4371i		−	0.803006i	0.915858	−	0.401503i	$-0.131512\pi$
$420$	−6.67714	+	11.2570i	−0.325811	+	0.549286i
$421$	10.0871	−	7.32873i	0.491617	−	0.357180i	−0.314189	−	0.949360i	$-0.601733\pi$
$421$	10.0871	−	7.32873i	0.491617	−	0.357180i	0.805806	+	0.592180i	$0.201733\pi$
$422$	−0.676498	−	4.27124i	−0.0329314	−	0.207921i
$423$	5.58277	+	2.84457i	0.271444	+	0.138308i
$424$	−0.838815	−	2.58161i	−0.0407364	−	0.125374i
$425$	−25.2754	−	7.41452i	−1.22604	−	0.359657i
$426$	0.939632	+	1.29329i	0.0455253	+	0.0626602i
$427$	−18.0289	+	9.18618i	−0.872479	+	0.444550i
$428$	−0.542488	−	0.542488i	−0.0262222	−	0.0262222i
$429$		0			0
$430$	−7.64304	−	1.71886i	−0.368580	−	0.0828907i
$431$	−18.8644	−	6.12941i	−0.908666	−	0.295243i	−0.182857	−	0.983140i	$-0.558534\pi$
$431$	−18.8644	−	6.12941i	−0.908666	−	0.295243i	−0.725809	+	0.687896i	$0.758534\pi$
$432$	−13.8947	−	2.20070i	−0.668508	−	0.105881i
$433$	28.2730	−	4.47800i	1.35871	−	0.215199i	0.565803	−	0.824540i	$-0.308566\pi$
$433$	28.2730	−	4.47800i	1.35871	−	0.215199i	0.792908	+	0.609341i	$0.208566\pi$
$434$	−9.13013	+	2.96656i	−0.438260	+	0.142399i
$435$	5.18593	+	4.30155i	0.248647	+	0.206243i
$436$	−9.80183	+	13.4911i	−0.469422	+	0.646104i
$437$	1.92307	−	12.1418i	0.0919929	−	0.580820i
$438$	3.73893	+	7.33807i	0.178653	+	0.350626i
$439$	3.12279			0.149043			0.0745214	−	0.997219i	$-0.476257\pi$
$439$	3.12279			0.149043			0.0745214	+	0.997219i	$0.476257\pi$
$440$		0			0
$441$	2.56208			0.122004
$442$	−3.41802	−	6.70823i	−0.162578	−	0.319078i
$443$	−4.96491	+	31.3472i	−0.235890	+	1.48935i	0.530890	+	0.847441i	$0.321858\pi$
$443$	−4.96491	+	31.3472i	−0.235890	+	1.48935i	−0.766780	+	0.641910i	$0.778142\pi$
$444$	−1.37231	+	1.88882i	−0.0651269	+	0.0896395i
$445$	−24.8749	+	2.31874i	−1.17918	+	0.109919i
$446$	−2.87126	+	0.932929i	−0.135958	+	0.0441755i
$447$	20.2306	−	3.20422i	0.956876	−	0.151554i
$448$	−8.15682	−	1.29191i	−0.385373	−	0.0610372i
$449$	−33.2818	−	10.8139i	−1.57067	−	0.510341i	−0.611036	−	0.791603i	$-0.709247\pi$
$449$	−33.2818	−	10.8139i	−1.57067	−	0.510341i	−0.959631	+	0.281262i	$0.909247\pi$
$450$	−1.39743	−	3.91340i	−0.0658753	−	0.184479i
$451$		0			0
$452$	−25.2437	−	25.2437i	−1.18736	−	1.18736i
$453$	−18.0622	+	9.20317i	−0.848638	+	0.432402i
$454$	0.952026	+	1.31035i	0.0446808	+	0.0614978i
$455$	12.6023	+	14.3320i	0.590805	+	0.671896i
$456$	2.65122	+	8.15963i	0.124155	+	0.382110i
$457$	−4.54419	−	2.31538i	−0.212568	−	0.108309i	0.344465	−	0.938799i	$-0.388060\pi$
$457$	−4.54419	−	2.31538i	−0.212568	−	0.108309i	−0.557033	+	0.830490i	$0.688060\pi$
$458$	0.407937	+	2.57562i	0.0190617	+	0.120351i
$459$	22.8319	−	16.5884i	1.06570	−	0.774279i
$460$	11.4446	−	2.92262i	0.533608	−	0.136268i
$461$		−	12.4703i		−	0.580801i	−0.956905	−	0.290400i	$-0.906211\pi$
$461$		−	12.4703i		−	0.580801i	0.956905	−	0.290400i	$-0.0937885\pi$
$462$		0			0
$463$	−19.2728	+	19.2728i	−0.895684	+	0.895684i	−0.995051	−	0.0993669i	$-0.968318\pi$
$463$	−19.2728	+	19.2728i	−0.895684	+	0.895684i	0.0993669	+	0.995051i	$0.468318\pi$
$464$	−2.14609	+	6.60498i	−0.0996297	+	0.306629i
$465$	6.34256	−	15.9588i	0.294129	−	0.740073i
$466$	1.74554	+	1.26821i	0.0808607	+	0.0587487i
$467$	−18.0203	+	35.3668i	−0.833879	+	1.63658i	−0.0643861	+	0.997925i	$0.520509\pi$
$467$	−18.0203	+	35.3668i	−0.833879	+	1.63658i	−0.769493	+	0.638655i	$0.779491\pi$
$468$	−3.98299	+	7.81705i	−0.184114	+	0.361343i
$469$	4.38683	+	3.18722i	0.202565	+	0.147172i
$470$	3.69168	−	1.59184i	0.170285	−	0.0734260i
$471$	7.55738	−	23.2592i	0.348226	−	1.07173i
$472$	2.08508	−	2.08508i	0.0959738	−	0.0959738i
$473$		0			0
$474$			8.48273i			0.389625i
$475$	14.0698	−	14.9050i	0.645569	−	0.683889i
$476$	21.8952	−	15.9078i	1.00357	−	0.729134i
$477$	−0.393417	−	2.48393i	−0.0180133	−	0.113732i
$478$	4.54819	+	2.31742i	0.208029	+	0.105996i
$479$	−11.8215	−	36.3828i	−0.540138	−	1.66237i	−0.732278	−	0.681006i	$-0.761543\pi$
$479$	−11.8215	−	36.3828i	−0.540138	−	1.66237i	0.192141	−	0.981367i	$-0.438457\pi$
$480$	−9.48238	+	8.33796i	−0.432810	+	0.380574i
$481$	2.00102	+	2.75417i	0.0912389	+	0.125580i
$482$	12.1214	−	6.17614i	0.552113	−	0.281316i
$483$	7.04599	+	7.04599i	0.320603	+	0.320603i
$484$		0			0
$485$	−12.0387	−	19.0246i	−0.546650	−	0.863863i
$486$	6.93598	+	2.25364i	0.314622	+	0.102227i
$487$	−26.8446	−	4.25177i	−1.21645	−	0.192666i	−0.484968	−	0.874532i	$-0.661169\pi$
$487$	−26.8446	−	4.25177i	−1.21645	−	0.192666i	−0.731477	+	0.681866i	$0.761169\pi$
$488$	−12.5877	+	1.99369i	−0.569817	+	0.0902501i
$489$	−11.2965	+	3.67046i	−0.510846	+	0.165984i
$490$	1.04951	−	1.26529i	0.0474120	−	0.0571598i
$491$	−2.33461	+	3.21331i	−0.105359	+	0.145015i	−0.858441	−	0.512912i	$-0.828567\pi$
$491$	−2.33461	+	3.21331i	−0.105359	+	0.145015i	0.753082	+	0.657927i	$0.228567\pi$
$492$	1.11627	−	7.04784i	0.0503253	−	0.317741i
$493$	−6.32512	−	12.4138i	−0.284869	−	0.559087i
$494$	5.85854			0.263588
$495$		0			0
$496$	17.7010			0.794798
$497$	3.80409	+	7.46596i	0.170637	+	0.334894i
$498$	0.581657	−	3.67244i	0.0260647	−	0.164566i
$499$	3.77656	−	5.19799i	0.169062	−	0.232694i	−0.716076	−	0.698022i	$-0.754064\pi$
$499$	3.77656	−	5.19799i	0.169062	−	0.232694i	0.885138	+	0.465328i	$0.154064\pi$
$500$	18.5040	+	6.74348i	0.827522	+	0.301577i
$501$	12.2369	−	3.97602i	0.546706	−	0.177636i
$502$	−4.79736	+	0.759827i	−0.214117	+	0.0339127i
$503$	−40.2254	−	6.37107i	−1.79356	−	0.284072i	−0.831224	−	0.555937i	$-0.812360\pi$
$503$	−40.2254	−	6.37107i	−1.79356	−	0.284072i	−0.962335	+	0.271865i	$0.912360\pi$
$504$	8.67089	+	2.81734i	0.386232	+	0.125494i
$505$	−0.936660	+	4.16493i	−0.0416808	+	0.185337i
$506$		0			0
$507$	3.57347	+	3.57347i	0.158703	+	0.158703i
$508$	−14.8002	+	7.54106i	−0.656651	+	0.334581i
$509$	−5.45800	−	7.51230i	−0.241922	−	0.332977i	0.670740	−	0.741693i	$-0.265977\pi$
$509$	−5.45800	−	7.51230i	−0.241922	−	0.332977i	−0.912662	+	0.408716i	$0.865977\pi$
$510$	0.420049	−	6.54078i	0.0186001	−	0.289630i
$511$	13.3398	+	41.0556i	0.590117	+	1.81619i
$512$	−20.1924	−	10.2886i	−0.892388	−	0.454695i
$513$	3.43542	+	21.6904i	0.151678	+	0.957654i
$514$	1.67530	−	1.21718i	0.0738944	−	0.0536875i
$515$	−3.41442	−	13.3704i	−0.150457	−	0.589171i
$516$			14.3987i			0.633868i
$517$		0			0
$518$	1.17149	−	1.17149i	0.0514723	−	0.0514723i
$519$	4.64826	−	14.3059i	0.204036	−	0.627958i
$520$	4.75956	+	11.0380i	0.208721	+	0.484050i
$521$	11.9792	+	8.70338i	0.524817	+	0.381302i	0.818416	−	0.574627i	$-0.194853\pi$
$521$	11.9792	+	8.70338i	0.524817	+	0.381302i	−0.293598	+	0.955929i	$0.594853\pi$
$522$	0.997836	−	1.95836i	0.0436741	−	0.0857152i
$523$	−17.6345	+	34.6096i	−0.771102	+	1.51337i	0.0848935	+	0.996390i	$0.472945\pi$
$523$	−17.6345	+	34.6096i	−0.771102	+	1.51337i	−0.855996	+	0.516983i	$0.827055\pi$
$524$	10.7122	+	7.78284i	0.467963	+	0.339995i
$525$	3.07075	+	16.3280i	0.134019	+	0.712612i
$526$	3.45364	−	10.6292i	0.150586	−	0.463456i
$527$	−25.1096	+	25.1096i	−1.09379	+	1.09379i
$528$		0			0
$529$			14.0073i			0.609011i
$530$	−1.38785	−	0.823211i	−0.0602845	−	0.0357580i
$531$	2.21021	−	1.60581i	0.0959148	−	0.0696862i
$532$	3.29448	+	20.8005i	0.142834	+	0.901817i
$533$	−9.27081	−	4.72371i	−0.401563	−	0.204607i
$534$	−1.92097	−	5.91214i	−0.0831285	−	0.255843i
$535$	−0.971870	−	0.0624135i	−0.0420176	−	0.00269837i
$536$	2.00747	+	2.76304i	0.0867095	+	0.119345i
$537$	−2.26054	+	1.15180i	−0.0975495	+	0.0497039i
$538$	7.89771	+	7.89771i	0.340495	+	0.340495i
$539$		0			0
$540$	−17.8309	+	11.2833i	−0.767320	+	0.485558i
$541$	16.5674	+	5.38306i	0.712286	+	0.231436i	0.642676	−	0.766138i	$-0.277824\pi$
$541$	16.5674	+	5.38306i	0.712286	+	0.231436i	0.0696106	+	0.997574i	$0.477824\pi$
$542$	0.670600	+	0.106213i	0.0288047	+	0.00456222i
$543$	4.87803	−	0.772603i	0.209336	−	0.0331556i
$544$	24.8318	−	8.06835i	1.06466	−	0.345928i
$545$	1.96471	+	21.0769i	0.0841588	+	0.902834i
$546$	−2.79127	+	3.84186i	−0.119455	+	0.164416i
$547$	6.13326	−	38.7239i	0.262239	−	1.65571i	−0.407565	−	0.913176i	$-0.633622\pi$
$547$	6.13326	−	38.7239i	0.262239	−	1.65571i	0.669804	−	0.742538i	$-0.266378\pi$
$548$	12.2911	+	24.1226i	0.525049	+	1.03047i
$549$	−11.8076			−0.503936
$550$		0			0
$551$	10.8414			0.461858
$552$	2.84931	+	5.59209i	0.121275	+	0.238015i
$553$	−6.95558	+	43.9158i	−0.295781	+	1.86749i
$554$	−4.09197	+	5.63211i	−0.173851	+	0.239285i
$555$	0.275069	+	2.95087i	0.0116760	+	0.125258i
$556$	−6.97329	+	2.26576i	−0.295733	+	0.0960896i
$557$	−36.2493	+	5.74133i	−1.53593	+	0.243268i	−0.866338	−	0.499459i	$-0.833532\pi$
$557$	−36.2493	+	5.74133i	−1.53593	+	0.243268i	−0.669595	+	0.742727i	$0.733532\pi$
$558$	−5.53305	−	0.876348i	−0.234232	−	0.0370988i
$559$	19.9678	+	6.48793i	0.844548	+	0.274410i
$560$	−14.4711	+	9.15725i	−0.611514	+	0.386964i
$561$		0			0
$562$	8.76280	+	8.76280i	0.369636	+	0.369636i
$563$	15.0411	−	7.66381i	0.633906	−	0.322991i	−0.107342	−	0.994222i	$-0.534234\pi$
$563$	15.0411	−	7.66381i	0.633906	−	0.322991i	0.741248	+	0.671231i	$0.234234\pi$
$564$	−4.34326	−	5.97799i	−0.182884	−	0.251719i
$565$	−45.2241	−	2.90429i	−1.90259	−	0.122185i
$566$	−1.11832	−	3.44182i	−0.0470063	−	0.144671i
$567$	−2.59368	−	1.32155i	−0.108924	−	0.0554997i
$568$	0.825608	+	5.21268i	0.0346417	+	0.218719i
$569$	−2.14294	+	1.55694i	−0.0898368	+	0.0652703i	−0.631797	−	0.775134i	$-0.717682\pi$
$569$	−2.14294	+	1.55694i	−0.0898368	+	0.0652703i	0.541960	+	0.840404i	$0.317682\pi$
$570$	4.38656	+	2.60191i	0.183733	+	0.108982i
$571$			29.8675i			1.24992i	0.780658	+	0.624959i	$0.214884\pi$
$571$			29.8675i			1.24992i	−0.780658	+	0.624959i	$0.785116\pi$
$572$		0			0
$573$	3.28527	−	3.28527i	0.137244	−	0.137244i
$574$	−1.56473	+	4.81574i	−0.0653105	+	0.201005i
$575$	8.46007	−	12.3792i	0.352809	−	0.516250i
$576$	−3.89881	−	2.83265i	−0.162450	−	0.118027i
$577$	−0.162935	+	0.319779i	−0.00678309	+	0.0133126i	−0.894373	−	0.447322i	$-0.852378\pi$
$577$	−0.162935	+	0.319779i	−0.00678309	+	0.0133126i	0.887590	+	0.460634i	$0.152378\pi$
$578$	−2.38394	+	4.67875i	−0.0991589	+	0.194610i
$579$	−19.2655	−	13.9972i	−0.800649	−	0.581705i
$580$	4.12465	+	9.56560i	0.171267	+	0.397190i
$581$	6.02257	−	18.5356i	0.249858	−	0.768985i
$582$	3.96123	−	3.96123i	0.164198	−	0.164198i
$583$		0			0
$584$			27.1896i			1.12511i
$585$	2.75557	+	10.7905i	0.113929	+	0.446130i
$586$	5.79867	−	4.21298i	0.239541	−	0.174037i
$587$	4.04336	+	25.5288i	0.166887	+	1.05368i	0.918887	+	0.394521i	$0.129090\pi$
$587$	4.04336	+	25.5288i	0.166887	+	1.05368i	−0.752000	+	0.659164i	$0.770910\pi$
$588$	−2.69216	−	1.37172i	−0.111023	−	0.0565690i
$589$	−8.53884	−	26.2798i	−0.351837	−	1.08284i
$590$	0.112341	−	1.74931i	0.00462499	−	0.0720178i
$591$	0.202473	+	0.278680i	0.00832861	+	0.0114634i
$592$	−2.72183	+	1.38684i	−0.111867	+	0.0569989i
$593$	9.56872	+	9.56872i	0.392940	+	0.392940i	0.875734	−	0.482794i	$-0.160378\pi$
$593$	9.56872	+	9.56872i	0.392940	+	0.392940i	−0.482794	+	0.875734i	$0.660378\pi$
$594$		0			0
$595$	7.53787	−	33.5177i	0.309022	−	1.37409i
$596$	30.1178	+	9.78585i	1.23367	+	0.400844i
$597$	12.4704	+	1.97512i	0.510381	+	0.0808364i
$598$	4.23291	−	0.670427i	0.173096	−	0.0274158i
$599$	10.7687	−	3.49896i	0.439997	−	0.142964i	−0.0806373	−	0.996744i	$-0.525696\pi$
$599$	10.7687	−	3.49896i	0.439997	−	0.142964i	0.520634	+	0.853780i	$0.325696\pi$
$600$	−1.33854	+	10.3785i	−0.0546456	+	0.423701i
$601$	9.69211	−	13.3401i	0.395350	−	0.544152i	−0.564220	−	0.825625i	$-0.690823\pi$
$601$	9.69211	−	13.3401i	0.395350	−	0.544152i	0.959569	+	0.281473i	$0.0908229\pi$
$602$	1.59837	−	10.0917i	0.0651446	−	0.411307i
$603$	1.43653	+	2.81934i	0.0584999	+	0.114812i
$604$	−31.3413			−1.27526
$605$		0			0
$606$	−1.06223			−0.0431503
$607$	2.26285	+	4.44109i	0.0918461	+	0.180258i	0.932359	−	0.361533i	$-0.117746\pi$
$607$	2.26285	+	4.44109i	0.0918461	+	0.180258i	−0.840513	+	0.541791i	$0.817746\pi$
$608$	−3.17832	+	20.0671i	−0.128898	+	0.813828i
$609$	−5.16532	+	7.10945i	−0.209309	+	0.288090i
$610$	−4.83678	+	5.83121i	−0.195835	+	0.236099i
$611$	−10.2472	+	3.32951i	−0.414556	+	0.134697i
$612$	15.5986	−	2.47057i	0.630536	−	0.0998670i
$613$	−18.0546	−	2.85957i	−0.729218	−	0.115497i	−0.219224	−	0.975675i	$-0.570352\pi$
$613$	−18.0546	−	2.85957i	−0.729218	−	0.115497i	−0.509994	+	0.860178i	$0.670352\pi$
$614$	0.574683	+	0.186726i	0.0231923	+	0.00753565i
$615$	−4.84357	−	7.65423i	−0.195312	−	0.308648i
$616$		0			0
$617$	15.4942	+	15.4942i	0.623773	+	0.623773i	0.946494	−	0.322721i	$-0.104598\pi$
$617$	15.4942	+	15.4942i	0.623773	+	0.623773i	−0.322721	+	0.946494i	$0.604598\pi$
$618$	3.05945	−	1.55887i	0.123069	−	0.0627068i
$619$	−28.9283	−	39.8164i	−1.16273	−	1.60036i	−0.700622	−	0.713533i	$-0.747094\pi$
$619$	−28.9283	−	39.8164i	−1.16273	−	1.60036i	−0.462106	−	0.886825i	$-0.652906\pi$
$620$	19.9387	−	17.5323i	0.800757	−	0.704114i
$621$	4.96431	+	15.2786i	0.199211	+	0.613109i
$622$	−6.15549	−	3.13638i	−0.246813	−	0.125757i
$623$	−5.09725	−	32.1828i	−0.204217	−	1.28938i
$624$	7.08383	−	5.14670i	0.283580	−	0.206033i
$625$	23.2920	−	9.08211i	0.931678	−	0.363284i
$626$		−	0.361199i		−	0.0144364i
$627$		0			0
$628$	26.7363	−	26.7363i	1.06689	−	1.06689i
$629$	1.89374	−	5.82832i	0.0755082	−	0.232390i
$630$	4.97678	−	2.14597i	0.198280	−	0.0854974i
$631$	7.32346	+	5.32080i	0.291542	+	0.211818i	0.723936	−	0.689867i	$-0.242331\pi$
$631$	7.32346	+	5.32080i	0.291542	+	0.211818i	−0.432394	+	0.901685i	$0.642331\pi$
$632$	−12.7141	+	24.9528i	−0.505739	+	0.992568i
$633$	−4.58058	+	8.98990i	−0.182062	+	0.357316i
$634$	6.74238	+	4.89863i	0.267774	+	0.194549i
$635$	−7.78754	+	19.5946i	−0.309039	+	0.777588i
$636$	−0.916496	+	2.82068i	−0.0363414	+	0.111847i
$637$	−3.11534	+	3.11534i	−0.123434	+	0.123434i
$638$		0			0
$639$			4.88965i			0.193432i
$640$	−24.4716	+	6.24932i	−0.967323	+	0.247026i
$641$	22.5944	−	16.4158i	0.892426	−	0.648385i	−0.0440836	−	0.999028i	$-0.514037\pi$
$641$	22.5944	−	16.4158i	0.892426	−	0.648385i	0.936509	+	0.350643i	$0.114037\pi$
$642$	−0.0379082	−	0.239343i	−0.00149612	−	0.00944611i
$643$	8.57987	+	4.37166i	0.338357	+	0.172401i	0.614910	−	0.788597i	$-0.289192\pi$
$643$	8.57987	+	4.37166i	0.338357	+	0.172401i	−0.276553	+	0.960999i	$0.589192\pi$
$644$	4.76065	+	14.6518i	0.187596	+	0.577361i
$645$	12.0694	+	13.7260i	0.475231	+	0.540459i
$646$	−6.19886	−	8.53199i	−0.243891	−	0.335687i
$647$	−27.5778	+	14.0516i	−1.08420	+	0.552425i	−0.902395	−	0.430910i	$-0.858193\pi$
$647$	−27.5778	+	14.0516i	−1.08420	+	0.552425i	−0.181801	+	0.983335i	$0.558193\pi$
$648$	−1.29645	−	1.29645i	−0.0509296	−	0.0509296i
$649$		0			0
$650$	6.45766	+	3.05928i	0.253290	+	0.119995i
$651$	21.3018	+	6.92139i	0.834885	+	0.271270i
$652$	−18.1378	−	2.87275i	−0.710332	−	0.112506i
$653$	6.03516	−	0.955876i	0.236174	−	0.0374063i	−0.0372253	−	0.999307i	$-0.511852\pi$
$653$	6.03516	−	0.955876i	0.236174	−	0.0374063i	0.273399	+	0.961901i	$0.411852\pi$
$654$	−5.00945	+	1.62767i	−0.195885	+	0.0636468i
$655$	16.7354	−	1.56002i	0.653908	−	0.0609548i
$656$	5.48785	−	7.55337i	0.214264	−	0.294910i
$657$	−3.94069	+	24.8805i	−0.153741	+	0.970682i
$658$	2.38048	+	4.67195i	0.0928008	+	0.182132i
$659$	−12.0647			−0.469975			−0.234988	−	0.971998i	$-0.575505\pi$
$659$	−12.0647			−0.469975			−0.234988	+	0.971998i	$0.575505\pi$
$660$		0			0
$661$	−29.6228			−1.15219			−0.576097	−	0.817382i	$-0.695425\pi$
$661$	−29.6228			−1.15219			−0.576097	+	0.817382i	$0.695425\pi$
$662$	−3.30754	−	6.49141i	−0.128551	−	0.252296i
$663$	−2.74789	+	17.3495i	−0.106719	+	0.673799i
$664$	7.21531	−	9.93103i	0.280008	−	0.385399i
$665$	20.5761	+	17.0671i	0.797907	+	0.661835i
$666$	0.919461	−	0.298751i	0.0356284	−	0.0115764i
$667$	7.83310	−	1.24064i	0.303299	−	0.0480378i
$668$	19.6478	+	3.11190i	0.760195	+	0.120403i
$669$	6.69903	+	2.17665i	0.259000	+	0.0841541i
$670$	1.98079	+	0.445463i	0.0765244	+	0.0172097i
$671$		0			0
$672$	−11.6451	−	11.6451i	−0.449220	−	0.449220i
$673$	−4.48693	+	2.28621i	−0.172958	+	0.0881267i	−0.538326	−	0.842736i	$-0.680943\pi$
$673$	−4.48693	+	2.28621i	−0.172958	+	0.0881267i	0.365368	+	0.930863i	$0.380943\pi$
$674$	2.70894	+	3.72853i	0.104344	+	0.143618i
$675$	−7.53979	+	25.7025i	−0.290207	+	0.989289i
$676$	2.41443	+	7.43084i	0.0928626	+	0.285802i
$677$	−32.4380	−	16.5280i	−1.24670	−	0.635223i	−0.298956	−	0.954267i	$-0.596638\pi$
$677$	−32.4380	−	16.5280i	−1.24670	−	0.635223i	−0.947740	+	0.319044i	$0.896638\pi$
$678$	−1.76398	−	11.1374i	−0.0677454	−	0.427728i
$679$	23.7557	−	17.2595i	0.911661	−	0.662360i
$680$	11.0390	−	18.6107i	0.423328	−	0.713690i
$681$		−	3.77894i		−	0.144809i
$682$		0			0
$683$	−8.07353	+	8.07353i	−0.308925	+	0.308925i	−0.844492	−	0.535567i	$-0.820098\pi$
$683$	−8.07353	+	8.07353i	−0.308925	+	0.308925i	0.535567	+	0.844492i	$0.320098\pi$
$684$	−3.79761	+	11.6878i	−0.145205	+	0.446895i
$685$	31.9370	+	12.6928i	1.22025	+	0.484968i
$686$	−6.33082	−	4.59961i	−0.241712	−	0.175614i
$687$	2.76215	−	5.42103i	0.105383	−	0.206825i
$688$	−8.55298	+	16.7862i	−0.326079	+	0.639967i
$689$	3.49870	+	2.54195i	0.133290	+	0.0968407i
$690$	3.46712	+	1.37795i	0.131991	+	0.0524576i
$691$	−3.67098	+	11.2981i	−0.139651	+	0.429801i	−0.996284	−	0.0861243i	$-0.972552\pi$
$691$	−3.67098	+	11.2981i	−0.139651	+	0.429801i	0.856634	+	0.515925i	$0.172552\pi$
$692$	16.4445	−	16.4445i	0.625125	−	0.625125i
$693$		0			0
$694$		−	9.39538i		−	0.356644i
$695$	−4.74826	+	8.00509i	−0.180112	+	0.303650i
$696$	−4.47789	+	3.25338i	−0.169734	+	0.123319i
$697$	2.93003	+	18.4995i	0.110983	+	0.700719i
$698$	−6.47142	−	3.29735i	−0.244947	−	0.124807i
$699$	−1.55559	−	4.78761i	−0.0588378	−	0.181084i
$700$	−7.23046	+	24.6480i	−0.273286	+	0.931608i
$701$	15.6038	+	21.4768i	0.589348	+	0.811169i	0.994681	−	0.103001i	$-0.0328444\pi$
$701$	15.6038	+	21.4768i	0.589348	+	0.811169i	−0.405333	+	0.914169i	$0.632844\pi$
$702$	−6.82157	+	3.47577i	−0.257464	+	0.131184i
$703$	3.37197	+	3.37197i	0.127176	+	0.127176i
$704$		0			0
$705$	−9.15124	−	2.05804i	−0.344655	−	0.0775102i
$706$	1.17180	+	0.380741i	0.0441012	+	0.0143294i
$707$	−5.49928	−	0.871000i	−0.206822	−	0.0327573i
$708$	−3.18217	+	0.504006i	−0.119593	+	0.0189417i
$709$	−16.9867	+	5.51933i	−0.637950	+	0.207283i	−0.610094	−	0.792329i	$-0.708868\pi$
$709$	−16.9867	+	5.51933i	−0.637950	+	0.207283i	−0.0278567	+	0.999612i	$0.508868\pi$
$710$	2.41477	+	2.00296i	0.0906245	+	0.0751698i
$711$	−15.2508	+	20.9909i	−0.571950	+	0.787222i
$712$	3.21050	−	20.2703i	0.120319	−	0.759662i
$713$	−9.17683	−	18.0105i	−0.343675	−	0.674500i
$714$	8.54844			0.319917
$715$		0			0
$716$	−3.92246			−0.146589
$717$	−5.40685	−	10.6115i	−0.201923	−	0.396295i
$718$	−0.648729	+	4.09591i	−0.0242103	+	0.152858i
$719$	19.2585	−	26.5071i	0.718222	−	0.988547i	−0.281359	−	0.959603i	$-0.590785\pi$
$719$	19.2585	−	26.5071i	0.718222	−	0.988547i	0.999581	−	0.0289450i	$-0.00921475\pi$
$720$	−9.95007	+	0.927509i	−0.370817	+	0.0345662i
$721$	17.1172	−	5.56173i	0.637479	−	0.207130i
$722$	−1.05881	+	0.167699i	−0.0394048	+	0.00624111i
$723$	−31.3495	−	4.96527i	−1.16590	−	0.184660i
$724$	7.26202	+	2.35957i	0.269891	+	0.0876929i
$725$	11.9501	+	5.66127i	0.443814	+	0.210254i
$726$		0			0
$727$	0.964903	+	0.964903i	0.0357863	+	0.0357863i	0.724773	−	0.688987i	$-0.241944\pi$
$727$	0.964903	+	0.964903i	0.0357863	+	0.0357863i	−0.688987	+	0.724773i	$0.741944\pi$
$728$	−13.9690	+	7.11758i	−0.517727	+	0.263795i
$729$	−11.7614	−	16.1882i	−0.435609	−	0.599564i
$730$	10.6731	+	12.1380i	0.395028	+	0.449247i
$731$	−11.6791	−	35.9446i	−0.431968	−	1.32946i
$732$	12.4071	+	6.32174i	0.458580	+	0.233658i
$733$	−1.84488	−	11.6481i	−0.0681422	−	0.430233i	−0.998049	−	0.0624374i	$-0.980113\pi$
$733$	−1.84488	−	11.6481i	−0.0681422	−	0.430233i	0.929907	−	0.367796i	$-0.119887\pi$
$734$	8.38724	−	6.09369i	0.309579	−	0.224922i
$735$	−3.71619	+	0.949007i	−0.137074	+	0.0350047i
$736$			14.8626i			0.547842i
$737$		0			0
$738$	−2.08937	+	2.08937i	−0.0769107	+	0.0769107i
$739$	13.3170	−	40.9856i	0.489875	−	1.50768i	−0.334919	−	0.942247i	$-0.608709\pi$
$739$	13.3170	−	40.9856i	0.489875	−	1.50768i	0.824794	−	0.565434i	$-0.191291\pi$
$740$	−1.69229	+	4.25805i	−0.0622098	+	0.156529i
$741$	−11.0583	−	8.03430i	−0.406235	−	0.295147i
$742$	0.955467	−	1.87521i	0.0350763	−	0.0688411i
$743$	17.2126	−	33.7816i	0.631468	−	1.23933i	−0.324509	−	0.945883i	$-0.605199\pi$
$743$	17.2126	−	33.7816i	0.631468	−	1.23933i	0.955977	−	0.293443i	$-0.0948010\pi$
$744$	11.4131	+	8.29213i	0.418426	+	0.304004i
$745$	36.9133	−	15.9169i	1.35240	−	0.583149i
$746$	0.549420	−	1.69094i	0.0201157	−	0.0619098i
$747$	8.04189	−	8.04189i	0.294237	−	0.294237i
$748$		0			0
$749$		−	1.27018i		−	0.0464114i
$750$	3.47645	+	5.15861i	0.126942	+	0.188366i
$751$	−28.2437	+	20.5203i	−1.03063	+	0.748795i	−0.968434	−	0.249269i	$-0.919810\pi$
$751$	−28.2437	+	20.5203i	−1.03063	+	0.748795i	−0.0621941	+	0.998064i	$0.519810\pi$
$752$	−1.51244	−	9.54914i	−0.0551528	−	0.348221i
$753$	10.0972	+	5.14480i	0.367964	+	0.187487i
$754$	1.16795	+	3.59457i	0.0425341	+	0.130907i
$755$	−29.8770	+	26.2711i	−1.08733	+	0.956104i
$756$	−16.1766	−	22.2652i	−0.588337	−	0.809777i
$757$	−30.7182	+	15.6517i	−1.11647	+	0.568870i	−0.912077	−	0.410019i	$-0.865522\pi$
$757$	−30.7182	+	15.6517i	−1.11647	+	0.568870i	−0.204393	+	0.978889i	$0.565522\pi$
$758$	−5.72618	−	5.72618i	−0.207984	−	0.207984i
$759$		0			0
$760$	9.00370	+	14.2284i	0.326598	+	0.516119i
$761$	−13.2335	−	4.29984i	−0.479716	−	0.155869i	0.0591701	−	0.998248i	$-0.481155\pi$
$761$	−13.2335	−	4.29984i	−0.479716	−	0.155869i	−0.538886	+	0.842379i	$0.681155\pi$
$762$	−5.18204	−	0.820754i	−0.187725	−	0.0297328i
$763$	−27.2690	+	4.31898i	−0.987203	+	0.156358i
$764$	6.83155	−	2.21970i	0.247157	−	0.0803061i
$765$	12.7989	−	15.4303i	0.462744	−	0.557883i
$766$	−3.25512	+	4.48028i	−0.117612	+	0.161879i
$767$	−0.734913	+	4.64006i	−0.0265362	+	0.167543i
$768$	0.0763239	+	0.149794i	0.00275410	+	0.00540523i
$769$	13.3273			0.480596			0.240298	−	0.970699i	$-0.422755\pi$
$769$	13.3273			0.480596			0.240298	+	0.970699i	$0.422755\pi$
$770$		0			0
$771$	−4.83143			−0.174000
$772$	−16.7146	−	32.8043i	−0.601573	−	1.18065i
$773$	−1.95537	+	12.3457i	−0.0703298	+	0.444045i	0.927246	+	0.374453i	$0.122170\pi$
$773$	−1.95537	+	12.3457i	−0.0703298	+	0.444045i	−0.997576	+	0.0695917i	$0.977830\pi$
$774$	3.50458	−	4.82364i	0.125970	−	0.173382i
$775$	4.31105	−	33.4263i	0.154858	−	1.20071i
$776$	17.5895	−	5.71518i	0.631427	−	0.205163i
$777$	−3.81780	+	0.604680i	−0.136963	+	0.0216928i
$778$	−0.394336	−	0.0624567i	−0.0141376	−	0.00223918i
$779$	−13.8614	−	4.50386i	−0.496638	−	0.161367i
$780$	2.88168	−	12.8136i	0.103181	−	0.458802i
$781$		0			0
$782$	−5.45516	−	5.45516i	−0.195076	−	0.195076i
$783$	−12.6235	+	6.43199i	−0.451127	+	0.229861i
$784$	−2.32373	−	3.19834i	−0.0829904	−	0.114227i
$785$	3.07602	−	47.8981i	0.109788	−	1.70956i
$786$	1.29240	+	3.97760i	0.0460984	+	0.141876i
$787$	−5.60690	−	2.85686i	−0.199864	−	0.101836i	0.351194	−	0.936303i	$-0.385776\pi$
$787$	−5.60690	−	2.85686i	−0.199864	−	0.101836i	−0.551058	+	0.834467i	$0.685776\pi$
$788$	0.0833119	+	0.526011i	0.00296786	+	0.0187384i
$789$	−21.0956	+	15.3269i	−0.751024	+	0.545651i
$790$	4.11919	+	16.1302i	0.146554	+	0.573888i
$791$		−	59.1055i		−	2.10155i
$792$		0			0
$793$	14.3574	−	14.3574i	0.509846	−	0.509846i
$794$	−2.52901	+	7.78350i	−0.0897512	+	0.276226i
$795$	1.49070	+	3.45712i	0.0528696	+	0.122612i
$796$	15.7923	+	11.4738i	0.559744	+	0.406678i
$797$	−0.802918	+	1.57581i	−0.0284408	+	0.0558182i	−0.904790	−	0.425859i	$-0.859972\pi$
$797$	−0.802918	+	1.57581i	−0.0284408	+	0.0558182i	0.876349	+	0.481677i	$0.159972\pi$
$798$	−3.01992	+	5.92693i	−0.106904	+	0.209811i
$799$	15.6913	+	11.4004i	0.555118	+	0.403317i
$800$	−13.9822	+	20.4596i	−0.494346	+	0.723355i
$801$	5.87569	−	18.0835i	0.207607	−	0.638950i
$802$	9.82669	−	9.82669i	0.346992	−	0.346992i
$803$		0			0
$804$		−	3.73160i		−	0.131603i
$805$	16.8197	+	9.97669i	0.592817	+	0.351632i
$806$	7.79346	−	5.66228i	0.274513	−	0.199445i
$807$	−4.07651	−	25.7381i	−0.143500	−	0.906023i
$808$	−3.12466	−	1.59210i	−0.109925	−	0.0560097i
$809$	5.70252	+	17.5505i	0.200490	+	0.617044i	0.999869	+	0.0162167i	$0.00516216\pi$
$809$	5.70252	+	17.5505i	0.200490	+	0.617044i	−0.799379	+	0.600828i	$0.794838\pi$
$810$	−1.08768	−	0.0698506i	−0.0382171	−	0.00245430i
$811$	7.66716	+	10.5529i	0.269230	+	0.370564i	0.922130	−	0.386881i	$-0.126448\pi$
$811$	7.66716	+	10.5529i	0.269230	+	0.370564i	−0.652899	+	0.757445i	$0.726448\pi$
$812$	−12.1056	+	6.16811i	−0.424823	+	0.216458i
$813$	−1.12013	−	1.12013i	−0.0392847	−	0.0392847i
$814$		0			0
$815$	−19.6984	+	12.4651i	−0.690004	+	0.436633i
$816$	−14.9906	−	4.87075i	−0.524777	−	0.170510i
$817$	29.0476	+	4.60068i	1.01625	+	0.160957i
$818$	−1.16852	+	0.185075i	−0.0408562	+	0.00647099i
$819$	−13.8143	+	4.48853i	−0.482710	+	0.156842i
$820$	−1.29979	−	13.9438i	−0.0453905	−	0.486938i
$821$	15.3089	−	21.0709i	0.534283	−	0.735378i	−0.453492	−	0.891260i	$-0.649822\pi$
$821$	15.3089	−	21.0709i	0.534283	−	0.735378i	0.987776	+	0.155882i	$0.0498220\pi$
$822$	−1.33774	+	8.44614i	−0.0466590	+	0.294593i
$823$	2.28095	+	4.47662i	0.0795089	+	0.156045i	0.927338	−	0.374224i	$-0.122091\pi$
$823$	2.28095	+	4.47662i	0.0795089	+	0.156045i	−0.847829	+	0.530269i	$0.822091\pi$
$824$	11.3361			0.394912
$825$		0			0
$826$	2.28625			0.0795488
$827$	−5.52543	−	10.8443i	−0.192138	−	0.377092i	0.774760	−	0.632255i	$-0.217871\pi$
$827$	−5.52543	−	10.8443i	−0.192138	−	0.377092i	−0.966898	+	0.255164i	$0.917871\pi$
$828$	−1.40634	+	8.87927i	−0.0488736	+	0.308576i
$829$	−6.47245	+	8.90857i	−0.224798	+	0.309407i	−0.906487	−	0.422235i	$-0.861246\pi$
$829$	−6.47245	+	8.90857i	−0.224798	+	0.309407i	0.681689	+	0.731642i	$0.261246\pi$
$830$	−0.677284	−	7.26572i	−0.0235089	−	0.252197i
$831$	15.4475	−	5.01921i	0.535869	−	0.174114i
$832$	8.18508	−	1.29639i	0.283766	−	0.0449442i
$833$	7.83329	+	1.24067i	0.271407	+	0.0429867i
$834$	−2.20259	−	0.715663i	−0.0762693	−	0.0247814i
$835$	21.3382	−	13.5028i	0.738440	−	0.467283i
$836$		0			0
$837$	25.5338	+	25.5338i	0.882578	+	0.882578i
$838$	7.15202	−	3.64414i	0.247062	−	0.125885i
$839$	5.46148	+	7.51708i	0.188551	+	0.259518i	0.892819	−	0.450416i	$-0.148724\pi$
$839$	5.46148	+	7.51708i	0.188551	+	0.259518i	−0.704268	+	0.709935i	$0.748724\pi$
$840$	−13.6203	−	0.874698i	−0.469946	−	0.0301800i
$841$	−6.80018	−	20.9288i	−0.234489	−	0.721683i
$842$	5.42516	+	2.76426i	0.186963	+	0.0952626i
$843$	−4.52303	−	28.5573i	−0.155782	−	0.983566i
$844$	−12.6200	+	9.16895i	−0.434397	+	0.315608i
$845$	8.53034	+	5.05981i	0.293453	+	0.174063i
$846$			3.05979i			0.105198i
$847$		0			0
$848$	−2.74398	+	2.74398i	−0.0942286	+	0.0942286i
$849$	−2.60918	+	8.03024i	−0.0895469	+	0.275597i
$850$	−2.37745	−	12.6415i	−0.0815457	−	0.433600i
$851$	2.82219	+	2.05044i	0.0967435	+	0.0702882i
$852$	2.61790	−	5.13791i	0.0896877	−	0.176022i
$853$	−12.2787	+	24.0984i	−0.420416	+	0.825113i	0.579532	+	0.814949i	$0.303235\pi$
$853$	−12.2787	+	24.0984i	−0.420416	+	0.825113i	−0.999948	+	0.0101637i	$0.996765\pi$
$854$	−7.99407	−	5.80803i	−0.273551	−	0.198747i
$855$	6.17688	+	14.3250i	0.211245	+	0.489904i
$856$	0.247221	−	0.760867i	0.00844983	−	0.0260059i
$857$	−33.1497	+	33.1497i	−1.13237	+	1.13237i	−0.142591	+	0.989782i	$0.545543\pi$
$857$	−33.1497	+	33.1497i	−1.13237	+	1.13237i	−0.989782	+	0.142591i	$0.954457\pi$
$858$		0			0
$859$		−	47.2517i		−	1.61221i	−0.591775	−	0.806103i	$-0.701573\pi$
$859$		−	47.2517i		−	1.61221i	0.591775	−	0.806103i	$-0.298427\pi$
$860$	6.99197	+	27.3797i	0.238424	+	0.933639i
$861$	9.55771	−	6.94409i	0.325726	−	0.236654i
$862$	−1.51527	−	9.56706i	−0.0516104	−	0.325855i
$863$	−13.8646	−	7.06437i	−0.471957	−	0.240474i	0.201801	−	0.979427i	$-0.435321\pi$
$863$	−13.8646	−	7.06437i	−0.471957	−	0.240474i	−0.673757	+	0.738953i	$0.735321\pi$
$864$	−8.20467	−	25.2514i	−0.279129	−	0.859070i
$865$	1.89194	−	29.4603i	0.0643280	−	1.00168i
$866$	8.21659	+	11.3092i	0.279211	+	0.384301i
$867$	10.9161	−	5.56205i	0.370732	−	0.188897i
$868$	24.4863	+	24.4863i	0.831118	+	0.831118i
$869$		0			0
$870$	−0.721933	+	3.21013i	−0.0244758	+	0.108834i
$871$	−5.17490	−	1.68143i	−0.175345	−	0.0569729i
$872$	−17.1753	−	2.72031i	−0.581630	−	0.0921212i
$873$	16.9240	−	2.68050i	0.572792	−	0.0907213i
$874$	5.70941	−	1.85510i	0.193124	−	0.0627496i
$875$	13.7680	+	29.5572i	0.465443	+	0.999214i
$876$	17.4617	−	24.0340i	0.589976	−	0.812032i
$877$	−4.55715	+	28.7727i	−0.153884	+	0.971586i	0.783019	+	0.621997i	$0.213679\pi$
$877$	−4.55715	+	28.7727i	−0.153884	+	0.971586i	−0.936903	+	0.349588i	$0.886321\pi$
$878$	0.692328	+	1.35877i	0.0233650	+	0.0458563i
$879$	−16.7229			−0.564048
$880$		0			0
$881$	4.18815			0.141102			0.0705512	−	0.997508i	$-0.477524\pi$
$881$	4.18815			0.141102			0.0705512	+	0.997508i	$0.477524\pi$
$882$	0.568016	+	1.11479i	0.0191261	+	0.0375371i
$883$	7.15185	−	45.1550i	0.240679	−	1.51959i	−0.510725	−	0.859744i	$-0.670623\pi$
$883$	7.15185	−	45.1550i	0.240679	−	1.51959i	0.751404	−	0.659843i	$-0.229377\pi$
$884$	−15.9629	+	21.9711i	−0.536892	+	0.738968i
$885$	−2.61102	+	3.14783i	−0.0877683	+	0.105813i
$886$	−14.7403	+	4.78942i	−0.495211	+	0.160904i
$887$	34.0342	−	5.39049i	1.14276	−	0.180995i	0.443777	−	0.896137i	$-0.353638\pi$
$887$	34.0342	−	5.39049i	1.14276	−	0.180995i	0.698979	+	0.715142i	$0.253638\pi$
$888$	−2.40464	−	0.380858i	−0.0806945	−	0.0127807i
$889$	−26.1549	−	8.49823i	−0.877206	−	0.285021i
$890$	−6.52371	−	10.3093i	−0.218675	−	0.345569i
$891$		0			0
$892$	7.70048	+	7.70048i	0.257831	+	0.257831i
$893$	−13.4476	+	6.85189i	−0.450006	+	0.229290i
$894$	5.87936	+	8.09224i	0.196635	+	0.270645i
$895$	−3.73919	+	3.28791i	−0.124987	+	0.109903i
$896$	−10.1795	−	31.3293i	−0.340073	−	1.04664i
$897$	−8.90922	−	4.53947i	−0.297470	−	0.151569i
$898$	−2.67335	−	16.8789i	−0.0892108	−	0.563255i
$899$	14.4220	−	10.4782i	0.481001	−	0.349467i
$900$	−10.2893	+	10.9000i	−0.342975	+	0.363333i
$901$		−	7.78489i		−	0.259352i
$902$		0			0
$903$	−16.8566	+	16.8566i	−0.560951	+	0.560951i
$904$	11.5039	−	35.4055i	0.382616	−	1.17757i
$905$	8.90057	−	3.83789i	0.295865	−	0.127576i
$906$	−8.00885	−	5.81877i	−0.266076	−	0.193316i
$907$	17.4845	−	34.3152i	0.580563	−	1.13942i	−0.394791	−	0.918771i	$-0.629183\pi$
$907$	17.4845	−	34.3152i	0.580563	−	1.13942i	0.975354	−	0.220648i	$-0.0708170\pi$
$908$	2.65243	−	5.20568i	0.0880239	−	0.172757i
$909$	−2.62855	−	1.90976i	−0.0871836	−	0.0633426i
$910$	−3.44211	+	8.66087i	−0.114105	+	0.287105i
$911$	−11.3933	+	35.0649i	−0.377476	+	1.16175i	0.564317	+	0.825558i	$0.309139\pi$
$911$	−11.3933	+	35.0649i	−0.377476	+	1.16175i	−0.941793	+	0.336193i	$0.890861\pi$
$912$	8.67283	−	8.67283i	0.287186	−	0.287186i
$913$		0			0
$914$		−	2.49056i		−	0.0823805i
$915$	17.1265	−	4.37360i	0.566183	−	0.144587i
$916$	7.61001	−	5.52900i	0.251442	−	0.182683i
$917$	3.42935	+	21.6521i	0.113247	+	0.715015i
$918$	12.2797	+	6.25682i	0.405291	+	0.206506i
$919$	9.39535	+	28.9159i	0.309924	+	0.953848i	0.977794	+	0.209570i	$0.0672063\pi$
$919$	9.39535	+	28.9159i	0.309924	+	0.953848i	−0.667870	+	0.744278i	$0.732794\pi$
$920$	8.13358	+	9.24995i	0.268156	+	0.304962i
$921$	−0.828668	−	1.14056i	−0.0273056	−	0.0375829i
$922$	5.42601	−	2.76469i	0.178696	−	0.0910502i
$923$	−5.94554	−	5.94554i	−0.195700	−	0.195700i
$924$		0			0
$925$	1.95599	+	5.47762i	0.0643126	+	0.180103i
$926$	−12.6587	−	4.11306i	−0.415990	−	0.135163i
$927$	10.3734	+	1.64298i	0.340707	+	0.0539626i
$928$	−12.9460	+	2.05045i	−0.424974	+	0.0673092i
$929$	22.1568	−	7.19917i	0.726940	−	0.236197i	0.0779103	−	0.996960i	$-0.475175\pi$
$929$	22.1568	−	7.19917i	0.726940	−	0.236197i	0.649029	+	0.760763i	$0.275175\pi$
$930$	8.35007	−	0.778362i	0.273809	−	0.0255235i
$931$	−3.62748	+	4.99280i	−0.118886	+	0.163632i
$932$	1.21751	−	7.68704i	0.0398808	−	0.251797i
$933$	7.31760	+	14.3616i	0.239567	+	0.470177i
$934$	−19.3837			−0.634254
$935$		0			0
$936$	−9.14869			−0.299034
$937$	−3.65168	−	7.16683i	−0.119295	−	0.234130i	0.823635	−	0.567120i	$-0.191942\pi$
$937$	−3.65168	−	7.16683i	−0.119295	−	0.234130i	−0.942930	+	0.332990i	$0.891942\pi$
$938$	−0.414236	+	2.61538i	−0.0135253	+	0.0853953i
$939$	−0.495342	+	0.681780i	−0.0161649	+	0.0222491i
$940$	−11.1618	−	9.25829i	−0.364057	−	0.301972i
$941$	45.5460	−	14.7988i	1.48476	−	0.482427i	0.549228	−	0.835673i	$-0.314922\pi$
$941$	45.5460	−	14.7988i	1.48476	−	0.482427i	0.935531	+	0.353245i	$0.114922\pi$
$942$	11.7959	−	1.86829i	0.384331	−	0.0608721i
$943$	−10.5306	−	1.66788i	−0.342922	−	0.0543136i
$944$	−4.00919	−	1.30266i	−0.130488	−	0.0423981i
$945$	−34.0840	−	7.66523i	−1.10875	−	0.249350i
$946$		0			0
$947$	9.38618	+	9.38618i	0.305010	+	0.305010i	0.842970	−	0.537960i	$-0.180805\pi$
$947$	9.38618	+	9.38618i	0.305010	+	0.305010i	−0.537960	+	0.842970i	$0.680805\pi$
$948$	27.2636	−	13.8915i	0.885481	−	0.451175i
$949$	−25.4617	−	35.0450i	−0.826521	−	1.13761i
$950$	9.60468	+	2.81752i	0.311617	+	0.0914124i
$951$	−6.00866	−	18.4928i	−0.194844	−	0.599669i
$952$	25.1461	+	12.8126i	0.814989	+	0.415257i
$953$	8.32956	+	52.5908i	0.269821	+	1.70358i	0.634890	+	0.772602i	$0.281045\pi$
$953$	8.32956	+	52.5908i	0.269821	+	1.70358i	−0.365069	+	0.930980i	$0.618955\pi$
$954$	0.993573	−	0.721873i	0.0321681	−	0.0233715i
$955$	4.65174	−	7.84238i	0.150527	−	0.253773i
$956$		−	18.4130i		−	0.595519i
$957$		0			0
$958$	13.2098	−	13.2098i	0.426790	−	0.426790i
$959$	−13.8512	+	42.6295i	−0.447277	+	1.37658i
$960$	6.70430	+	2.66451i	0.216380	+	0.0859966i
$961$	−11.6790	−	8.48526i	−0.376741	−	0.273718i
$962$	−0.754749	+	1.48128i	−0.0243341	+	0.0477583i
$963$	0.336501	−	0.660420i	0.0108436	−	0.0212817i
$964$	−39.7004	−	28.8440i	−1.27866	−	0.929004i
$965$	−43.4312	−	17.2610i	−1.39810	−	0.555650i
$966$	−1.50370	+	4.62791i	−0.0483807	+	0.148901i
$967$	38.6475	−	38.6475i	1.24282	−	1.24282i	0.283994	−	0.958826i	$-0.408340\pi$
$967$	38.6475	−	38.6475i	1.24282	−	1.24282i	0.958826	−	0.283994i	$-0.0916596\pi$
$968$		0			0
$969$			24.6055i			0.790443i
$970$	5.60887	−	9.45599i	0.180090	−	0.303614i
$971$	−6.69055	+	4.86097i	−0.214710	+	0.155996i	−0.689942	−	0.723865i	$-0.742364\pi$
$971$	−6.69055	+	4.86097i	−0.214710	+	0.155996i	0.475232	+	0.879860i	$0.342364\pi$
$972$	−4.11529	−	25.9829i	−0.131998	−	0.833403i
$973$	−10.8161	−	5.51110i	−0.346750	−	0.176678i
$974$	−4.10149	−	12.6231i	−0.131420	−	0.404470i
$975$	−7.99369	−	14.6304i	−0.256003	−	0.468549i
$976$	10.7092	+	14.7399i	0.342792	+	0.471813i
$977$	48.7867	−	24.8581i	1.56083	−	0.795280i	0.561348	−	0.827580i	$-0.310283\pi$
$977$	48.7867	−	24.8581i	1.56083	−	0.795280i	0.999478	+	0.0322997i	$0.0102831\pi$
$978$	−4.10153	−	4.10153i	−0.131152	−	0.131152i
$979$		0			0
$980$	−5.78535	−	1.30108i	−0.184806	−	0.0415614i
$981$	−15.3225	−	4.97857i	−0.489208	−	0.158953i
$982$	−1.91574	−	0.303424i	−0.0611338	−	0.00968265i
$983$	−13.4712	+	2.13363i	−0.429664	+	0.0680521i	−0.367521	−	0.930015i	$-0.619793\pi$
$983$	−13.4712	+	2.13363i	−0.429664	+	0.0680521i	−0.0621429	+	0.998067i	$0.519793\pi$
$984$	7.07684	−	2.29941i	0.225602	−	0.0733024i
$985$	0.520335	+	0.431600i	0.0165793	+	0.0137519i
$986$	3.99911	−	5.50430i	0.127357	−	0.175293i
$987$	1.91377	−	12.0831i	0.0609160	−	0.384608i
$988$	−9.59407	−	18.8294i	−0.305228	−	0.599044i
$989$	21.5139			0.684102
$990$		0			0
$991$	6.43457			0.204401			0.102200	−	0.994764i	$-0.467412\pi$
$991$	6.43457			0.204401			0.102200	+	0.994764i	$0.467412\pi$
$992$	15.1668	+	29.7666i	0.481547	+	0.945090i
$993$	−2.65908	+	16.7887i	−0.0843832	+	0.532775i
$994$	−2.40517	+	3.31043i	−0.0762872	+	0.105000i
$995$	24.6721	−	2.29984i	0.782158	−	0.0729099i
$996$	−12.7558	+	4.14461i	−0.404183	+	0.131327i
$997$	21.0146	−	3.32838i	0.665538	−	0.105411i	0.185481	−	0.982648i	$-0.440616\pi$
$997$	21.0146	−	3.32838i	0.665538	−	0.105411i	0.480058	+	0.877237i	$0.340616\pi$
$998$	3.09899	+	0.490831i	0.0980967	+	0.0155370i
$999$	−5.92680	−	1.92573i	−0.187516	−	0.0609275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.c.112.3		32
5.3	odd	4	inner	605.2.m.c.233.3		32
11.2	odd	10		55.2.l.a.52.2	yes	32
11.3	even	5		55.2.l.a.7.3	✓	32
11.4	even	5		605.2.e.b.362.8		32
11.5	even	5		605.2.m.d.457.2		32
11.6	odd	10	inner	605.2.m.c.457.3		32
11.7	odd	10		605.2.e.b.362.9		32
11.8	odd	10		605.2.m.e.282.2		32
11.9	even	5		605.2.m.e.602.3		32
11.10	odd	2		605.2.m.d.112.2		32
33.2	even	10		495.2.bj.a.217.3		32
33.14	odd	10		495.2.bj.a.172.2		32
44.3	odd	10		880.2.cm.a.337.2		32
44.35	even	10		880.2.cm.a.657.3		32
55.2	even	20		275.2.bm.b.118.2		32
55.3	odd	20		55.2.l.a.18.2	yes	32
55.8	even	20		605.2.m.e.403.3		32
55.13	even	20		55.2.l.a.8.3	yes	32
55.14	even	10		275.2.bm.b.7.2		32
55.18	even	20		605.2.e.b.483.8		32
55.24	odd	10		275.2.bm.b.107.3		32
55.28	even	20	inner	605.2.m.c.578.3		32
55.38	odd	20		605.2.m.d.578.2		32
55.43	even	4		605.2.m.d.233.2		32
55.47	odd	20		275.2.bm.b.18.3		32
55.48	odd	20		605.2.e.b.483.9		32
55.53	odd	20		605.2.m.e.118.2		32
165.68	odd	20		495.2.bj.a.118.2		32
165.113	even	20		495.2.bj.a.73.3		32
220.3	even	20		880.2.cm.a.513.3		32
220.123	odd	20		880.2.cm.a.833.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.3	✓	32	11.3	even	5
55.2.l.a.8.3	yes	32	55.13	even	20
55.2.l.a.18.2	yes	32	55.3	odd	20
55.2.l.a.52.2	yes	32	11.2	odd	10
275.2.bm.b.7.2		32	55.14	even	10
275.2.bm.b.18.3		32	55.47	odd	20
275.2.bm.b.107.3		32	55.24	odd	10
275.2.bm.b.118.2		32	55.2	even	20
495.2.bj.a.73.3		32	165.113	even	20
495.2.bj.a.118.2		32	165.68	odd	20
495.2.bj.a.172.2		32	33.14	odd	10
495.2.bj.a.217.3		32	33.2	even	10
605.2.e.b.362.8		32	11.4	even	5
605.2.e.b.362.9		32	11.7	odd	10
605.2.e.b.483.8		32	55.18	even	20
605.2.e.b.483.9		32	55.48	odd	20
605.2.m.c.112.3		32	1.1	even	1	trivial
605.2.m.c.233.3		32	5.3	odd	4	inner
605.2.m.c.457.3		32	11.6	odd	10	inner
605.2.m.c.578.3		32	55.28	even	20	inner
605.2.m.d.112.2		32	11.10	odd	2
605.2.m.d.233.2		32	55.43	even	4
605.2.m.d.457.2		32	11.5	even	5
605.2.m.d.578.2		32	55.38	odd	20
605.2.m.e.118.2		32	55.53	odd	20
605.2.m.e.282.2		32	11.8	odd	10
605.2.m.e.403.3		32	55.8	even	20
605.2.m.e.602.3		32	11.9	even	5
880.2.cm.a.337.2		32	44.3	odd	10
880.2.cm.a.513.3		32	220.3	even	20
880.2.cm.a.657.3		32	44.35	even	10
880.2.cm.a.833.2		32	220.123	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.221702 + 0.435114i) q^{2} +(0.178235 - 1.12533i) q^{3} +(1.03540 - 1.42510i) q^{4} +(-0.207538 - 2.22642i) q^{5} +(0.529164 - 0.171936i) q^{6} +(2.88051 - 0.456227i) q^{7} +(1.81429 + 0.287355i) q^{8} +(1.61856 + 0.525902i) q^{9} +(0.922733 - 0.583903i) q^{10} +(-1.41917 - 1.41917i) q^{12} +(-2.60754 + 1.32861i) q^{13} +(0.837124 + 1.15220i) q^{14} +(-2.54245 - 0.163276i) q^{15} +(-0.811484 - 2.49749i) q^{16} +(4.69392 + 2.39167i) q^{17} +(0.130010 + 0.820851i) q^{18} +(-3.31646 + 2.40955i) q^{19} +(-3.38776 - 2.00946i) q^{20} -3.32285i q^{21} +(-2.12046 + 2.12046i) q^{23} +(0.646740 - 1.99046i) q^{24} +(-4.91386 + 0.924132i) q^{25} +(-1.15619 - 0.840024i) q^{26} +(2.43208 - 4.77322i) q^{27} +(2.33230 - 4.57740i) q^{28} +(-2.13957 - 1.55449i) q^{29} +(-0.492622 - 1.14246i) q^{30} +(-2.08297 + 6.41071i) q^{31} +(3.50456 - 3.50456i) q^{32} +2.57262i q^{34} +(-1.61357 - 6.31852i) q^{35} +(2.42532 - 1.76210i) q^{36} +(-0.181976 - 1.14895i) q^{37} +(-1.78369 - 0.908835i) q^{38} +(1.03037 + 3.17117i) q^{39} +(0.263237 - 4.09899i) q^{40} +(2.08980 + 2.87636i) q^{41} +(1.44582 - 0.736681i) q^{42} +(-5.07292 - 5.07292i) q^{43} +(0.834964 - 3.71273i) q^{45} +(-1.39275 - 0.452533i) q^{46} +(3.63636 + 0.575943i) q^{47} +(-2.95515 + 0.468049i) q^{48} +(1.43178 - 0.465213i) q^{49} +(-1.49151 - 1.93320i) q^{50} +(3.52805 - 4.85594i) q^{51} +(-0.806440 + 5.09166i) q^{52} +(-0.670880 - 1.31668i) q^{53} +2.61609 q^{54} +5.35716 q^{56} +(2.12044 + 4.16159i) q^{57} +(0.202033 - 1.27559i) q^{58} +(0.943564 - 1.29870i) q^{59} +(-2.86514 + 3.45420i) q^{60} +(-6.59851 + 2.14398i) q^{61} +(-3.25119 + 0.514937i) q^{62} +(4.90220 + 0.776433i) q^{63} +(-2.69314 - 0.875053i) q^{64} +(3.49920 + 5.52974i) q^{65} +(1.31471 + 1.31471i) q^{67} +(8.26845 - 4.21298i) q^{68} +(2.00829 + 2.76417i) q^{69} +(2.39155 - 2.10291i) q^{70} +(0.887847 + 2.73251i) q^{71} +(2.78541 + 1.41924i) q^{72} +(2.31553 + 14.6197i) q^{73} +(0.459581 - 0.333905i) q^{74} +(0.164135 + 5.69444i) q^{75} +7.22113i q^{76} +(-1.15138 + 1.15138i) q^{78} +(-4.71123 + 14.4997i) q^{79} +(-5.39204 + 2.32503i) q^{80} +(-0.807503 - 0.586685i) q^{81} +(-0.788233 + 1.54699i) q^{82} +(3.03387 - 5.95431i) q^{83} +(-4.73540 - 3.44047i) q^{84} +(4.35068 - 10.9470i) q^{85} +(1.08262 - 3.33197i) q^{86} +(-2.13066 + 2.13066i) q^{87} -11.1726i q^{89} +(1.80057 - 0.459814i) q^{90} +(-6.90490 + 5.01670i) q^{91} +(0.826356 + 5.21741i) q^{92} +(6.84294 + 3.48665i) q^{93} +(0.555586 + 1.70992i) q^{94} +(6.05294 + 6.88374i) q^{95} +(-3.31916 - 4.56843i) q^{96} +(8.97103 - 4.57097i) q^{97} +(0.519848 + 0.519848i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{3} - 2 q^{5} - 20 q^{7} + 20 q^{8} + 12 q^{12} + 20 q^{13} + 4 q^{15} + 12 q^{16} - 30 q^{18} + 16 q^{20} - 24 q^{23} - 24 q^{25} - 20 q^{26} + 24 q^{27} + 20 q^{28} - 40 q^{30} + 32 q^{31}+ \cdots - 38 q^{97}+O(q^{100}) \) 32 * q + 6 * q^3 - 2 * q^5 - 20 * q^7 + 20 * q^8 + 12 * q^12 + 20 * q^13 + 4 * q^15 + 12 * q^16 - 30 * q^18 + 16 * q^20 - 24 * q^23 - 24 * q^25 - 20 * q^26 + 24 * q^27 + 20 * q^28 - 40 * q^30 + 32 * q^31 - 30 * q^35 - 36 * q^36 - 8 * q^37 + 10 * q^38 + 50 * q^40 - 20 * q^42 - 28 * q^45 - 20 * q^46 + 42 * q^47 + 26 * q^48 - 80 * q^50 + 100 * q^51 + 20 * q^52 - 34 * q^53 - 80 * q^56 + 40 * q^57 + 90 * q^58 - 86 * q^60 - 10 * q^62 + 10 * q^63 - 8 * q^67 + 70 * q^68 + 10 * q^70 - 36 * q^71 + 70 * q^72 - 30 * q^73 + 4 * q^75 + 60 * q^78 - 102 * q^80 + 8 * q^81 + 20 * q^82 + 60 * q^83 - 60 * q^85 - 80 * q^86 - 130 * q^90 - 60 * q^91 + 42 * q^92 - 8 * q^93 + 30 * q^95 - 38 * q^97

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